Projects & Practices in Physics 184_notes

184_notes:ac

Anonymous (anonymous@undisclosed.example.com) — 2021-07-13T13:30:22+00:00

Section 22.2 in Matter and Interactions (4th edition) Changing Flux from an Alternating Current As we said before, one of the most important sources of a changing magnetic field is an alternating current. This is what actually comes out of the wall outlets; as opposed to the current from a battery which is a constant current (or a direct current). We are only briefly going to talk about alternating current as it refers to induction and changing magnetic flux, but there are many more applicatio…

184_notes:access_template

Anonymous (anonymous@undisclosed.example.com) — 2022-03-24T13:41:46+00:00

Accessible Notes - Template These notes are to provide the standard practices & formats that should be used to improve the accessibility of any new notes on the EM/P-Cubed wiki pages. Text 1. Consistent use of headings 2. Consistent use of bold, italics, & underline

184_notes:amp_law

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T13:29:34+00:00

Section 21.6 in Matter and Interactions (4th edition) Putting Ampere's Law together Now, that we have built the two sides of Ampere's law, let's review the steps and put everything together to find the magnetic field outside of a long straight wire. This model of a long straight wire is usually pretty good for many situations where you want to determine the magnetic field near the wire. When you start to get farther away from the wire, the ends of the wire become problematic since the magnetic…

184_notes:assump

Anonymous (anonymous@undisclosed.example.com) — 2024-09-12T15:33:47+00:00

Assumptions & Approximations Making assumptions and approximations are a critical part of scientific modeling. The real world is very complex, so we are often creating a simplified model to explain, predict, and describe physical phenomena. Assumptions and approximations are a critical part of this process because they highlight what you are considering relevant and what you are considering as unimportant or negligible.

184_notes:b_current

Anonymous (anonymous@undisclosed.example.com) — 2021-07-07T15:29:22+00:00

Sections 17.2 and 17.6-17.8 in Matter and Interactions (4th edition) Currents Make Magnetic Fields Now that we have talked about a single moving charge and permanent magnets, the next source of magnetic fields that we are going to consider is currents (either comprised of electrons or some other charged particle). This builds on what we learned about $$\vec{B}_{tot}=\frac{\mu_0}{4 \pi}\frac{q_1\vec{v}\times \hat{r_1}}{r_1^2}+\frac{\mu_0}{4 \pi}\frac{q_2\vec{v}\times \hat{r_2}}{r_2^2}+\frac{\mu…

184_notes:b_flux_t

Anonymous (anonymous@undisclosed.example.com) — 2021-07-13T12:40:52+00:00

Section 22.2 in Matter and Interactions (4th edition) Changing Magnetic Fields with Time So far, we talked about how you can create a curly electric field (and thus an induced voltage/induced current) from a changing magnetic flux. We have gone through examples of what happens when the area changes and in your last project you worked through what happens when the coil is rotating. You also had a demo video that showed what happened when a strong magnet was brought towards or away from the coil…

184_notes:b_flux

Anonymous (anonymous@undisclosed.example.com) — 2021-06-17T16:08:41+00:00

Section 22.2 in Matter and Interactions (4th edition) Changing Magnetic Flux In these notes, we will start thinking the right hand side of Faraday's Law (the $\frac{d\Phi_{B}}{dt}$ part) and what it means to have a changing magnetic flux. Let's start by defining what flux is. $$\Phi_{B}= \vec{B} \bullet \vec{A}$$$\Phi_{B}$$T \cdot m^2$$\vec{B}$$\vec{A}$$+y$$-y$$\vec{B}$$\vec{A}$$$\Phi_{B}= |\vec{B}| |\vec{A}| cos(\theta)$$$\theta$$cos(\theta)=1$$cos(90) = 0$$$\Phi_B = \int \vec{B} \bullet d\ve…

184_notes:b_shapes

Anonymous (anonymous@undisclosed.example.com) — 2021-06-16T19:24:30+00:00

Shapes of Wires and Magnetic Fields Thus far, we have primarily been talking about the magnetic field from a current in a long, straight wire. However, there are many shapes of wire in the real world that do not correspond to straight wires. Particularly relevant to this class will be a coil of wire and something we will call a solenoid. These notes go more into detail about what coils and solenoids are, and what the magnetic field looks like from both coils and solenoids.$dl$$$\vec{B}_{tot}= \…

184_notes:b_summary

Anonymous (anonymous@undisclosed.example.com) — 2021-06-16T22:14:07+00:00

Summary of Magnetic Fields and Force It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon). $$\vec{B} = \dfrac{\mu_0}{4\pi} \dfrac{q \vec{v} \times \hat{r}}{r^2}$$$$\vec{B} = \dfrac{\mu_0}{4 \pi} \int \dfrac{I d\vec{l} \times \hat{r}}{r^2…

184_notes:b_sup_comp

Anonymous (anonymous@undisclosed.example.com) — 2021-06-16T19:16:22+00:00

Using Superposition of Magnetic Field and the Computer In the previous page of notes, we talked about how you can use superposition to calculate the magnetic field from a current rather than thinking about each individual moving charge. We ended up with an equation for the magnetic field where$$\vec{B}_{tot}= \int \frac{\mu_0}{4 \pi}\frac{I \cdot d\vec{l}\times \hat{r}}{r^2}$$$I$$d\vec{l}$$\vec{r}$$$\vec{B}_{net} = \sum \vec{B}_i = \vec{B}_1 + \vec{B}_2 + \vec{B}_3 + \dots$$$\vec{B}_1$$\vec{B}_…

184_notes:batteries

Anonymous (anonymous@undisclosed.example.com) — 2021-02-16T20:09:02+00:00

Part of Section 18.4 in Matter and Interactions (4th edition) Batteries While a pair of charged plates is easy to think about on a general level, it becomes surprisingly complicated to model at a microscopic level. As electrons move from one plate to the other, the amount of excess charge on each plate decreases, which means that over time, the

184_notes:c_parallel

Anonymous (anonymous@undisclosed.example.com) — 2021-03-18T03:07:09+00:00

Section 19.1 in Matter and Interactions (4th edition) Capacitors in Parallel The final combination that we will talk about will be capacitors in parallel. This section should feel familiar to the resistors in parallel. We will continue to use the loop and node rules to analyze these circuits, with our assumption that potential differences across the wires are negligible.$$Q_{bat}=Q_{C1}+Q_{C2}$$$$+|\Delta V_{bat}| - |\Delta V_{C1}| = 0$$$$|\Delta V_{bat}|=|\Delta V_{C1}|$$$$+|\Delta V_{bat}| -…

184_notes:c_series

Anonymous (anonymous@undisclosed.example.com) — 2021-06-28T23:54:26+00:00

Section 19.1 in Matter and Interactions (4th edition) Capacitors in Series Just like resistors, we are now moving to more of a macroscopic picture of capacitors, rather than thinking microscopically about the charges on the plates. These notes will talk about combinations of capacitors in series and how this differs from resistors in series. $$Q_1=Q_2$$$$+|\Delta V_{bat}|-|\Delta V_{C1}|-|\Delta V_{C2}|=0$$$$|\Delta V_{bat}|=|\Delta V_{C1}|+|\Delta V_{C2}|$$$C_1$$C_2$$C_e$$$|\Delta V_{bat}|=|\…

184_notes:cap_charging

Anonymous (anonymous@undisclosed.example.com) — 2022-10-19T14:40:11+00:00

Section 19.1 in Matter and Interactions (4th edition) Charging and Discharging Capacitors Over the last two weeks we have been building a fairly robust model of what happens to the charges both on the surface of the wires and those moving through the wire (through resistors). Now we are going to introduce a new circuit element called a capacitor and see what changes about the electron current, the electric field and the surface charges.

184_notes:cap_discharge

Anonymous (anonymous@undisclosed.example.com) — 2017-07-17T20:02:32+00:00

Capacitors and Discharging Last week, we talked about Gauss's law. In the project you found the electric field and electric potential between two parallel sheets of charge. If we increase the amount of charge on the plate - E-field and voltage would increase. These notes will talk about the ratio of charge to voltage, called capacitance, and what would happen if you connect a conducting wire between the plates.

184_notes:cap_in_cir

Anonymous (anonymous@undisclosed.example.com) — 2021-06-15T00:35:24+00:00

Section 19.1 in Matter and Interactions (4th edition) Capacitors in a Circuit As you read about, capacitors can be charged in a circuit and discharged through a resistor or lightbulb; thus, providing energy or powering a lightbulb for very short amounts of time. It turns out that this is a very useful circuit element and can be used for a variety of purposes in circuits. For example, a capacitor is used to provide power for a camera flash, provides a back up power supply for a computer (so it …

184_notes:changing_e

Anonymous (anonymous@undisclosed.example.com) — 2021-07-22T13:47:00+00:00

Section 23.1 in Matter and Interactions (4th edition) Changing Electric Fields We have spent the last two weeks talking about what happens when you have a changing magnetic field. We found that this changing magnetic field creates a curly electric field. A changing magnetic field then became another source of electric fields. You may then be wondering what happens if you have a changing electric field? We have already seen through Faraday's Law that electric and magnetic fields are related, so…

184_notes:charge_and_matter

Anonymous (anonymous@undisclosed.example.com) — 2021-01-25T00:06:26+00:00

Sections 14.1-14.7 in Matter and Interactions (4th edition) Charges and Matter Ordinary matter (of all varieties) is composed of charged particles. Every atom is made up of some combination of protons and electrons. In these notes, we will add charged particles to our microscopic model of matter and discuss some of the applications of this model.$+1.602 \cdot 10^{-19} \text{ C}$$-1.602 \cdot 10^{-19} \text{ C}$$0 \text{ C}$$\text{Na}^+$$\text{Cl}^-$

184_notes:charge

Anonymous (anonymous@undisclosed.example.com) — 2021-01-24T23:42:23+00:00

Section 3.1 and 3.7 in Matter and Interactions (4th edition) Electric Interaction The electric interaction is one of the fundamental ways that objects interact in the universe, and we observe its effects every day. The electric interaction is responsible for molecular bonding, keeping objects from falling through surfaces (also known as $-1.602 \cdot 10^{-19} C$$1 \cdot 10^{-7} C$$|1 e| = 1.602 \cdot 10^{-19} C$$$Q_{surroundings} = Q_{after}-Q_{before}=\Delta Q$$$Q_{surroundings}=0$$$Q_{before…

184_notes:charging_discharging

Anonymous (anonymous@undisclosed.example.com) — 2021-01-25T01:07:03+00:00

Charging and Discharging Using our microscopic model of the atom, we can now talk about how objects become charged (called charging) and how they return to being neutral (often called discharging). These notes will discuss how these processes occur and how they are different for insulators and conductors. $t=t_0$$t=t_1$$t=t_2$$t=t_3$

184_notes:charging

Anonymous (anonymous@undisclosed.example.com) — 2017-05-31T13:09:37+00:00

Charges and Matter Charging How we charge things Discharging Ground Conductors and Insulators

184_notes:combinations

Anonymous (anonymous@undisclosed.example.com) — 2021-11-23T21:09:09+00:00

Larger Combinations of Circuit Elements Now that you know about series and parallel combinations (both of resistors and capacitors), you can also make larger combinations in a circuit involving both series and parallel relationships. These relationships are foundational for the types of circuits that power all electronics (from your cell phone to NASA space station). Depending on the set up of your circuit and what you want the circuit to do, these circuits can get quite complicated. These note…

184_notes:comp_process

Anonymous (anonymous@undisclosed.example.com) — 2022-04-20T15:55:17+00:00

Coding: Group Process for Computational Projects Our in-class coding projects are unique, and require different group strategies than an analytical or design project. In this page of notes, we'll lay out some strategies for success when coding with your group.

184_notes:comp_super

Anonymous (anonymous@undisclosed.example.com) — 2021-02-09T19:08:50+00:00

Section 15.9 in Matter and Interactions (4th edition) Superposition and the Computer The principle of superposition is an overarching and powerful tool in much of physics. It is useful well beyond the electric field as you will see with the magnetic field (and as you might see in future physics courses in quantum mechanics). The fact that the electric field obeys the principle of superposition means we can define a powerful algorithm for computing the electric field at any given location from …

184_notes:conservation_theorems

Anonymous (anonymous@undisclosed.example.com) — 2021-07-06T17:36:44+00:00

Chapters 18 and 19 (and Chapters 2, 3, 6, 11, and 13) in Matter and Interactions (4th edition) Conservation Theorems Conservation theorems are central to many aspects of physics: they often form the central reasoning principles for new observations, they provide checks on new predictions, and they appear to be obeyed regardless of system and scale. You might not have heard them called conservation theorems before, but you have used them. In mechanics, these theorems manifest themselves as the …

184_notes:current

Anonymous (anonymous@undisclosed.example.com) — 2021-06-08T00:45:11+00:00

Sections 17.5 and 18.2 in Matter and Interactions (4th edition) Current in Wires In the last few pages of notes, we established that when connected to a battery there are surface charges in the wire that create a constant electric field through the wire. Because electric force is directly proportional to the electric field ($\vec{F} = q\vec{E}$), the electric field in the wire pushes the electrons from the negative plate of the battery to the positive plate of the battery causing an $$Q_{in}=Q…

184_notes:defining_a_system

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T19:30:58+00:00

Defining A System Choosing a system is one of the most important choices you make (either explicitly or implicitly) when investigating a physical situation. What we define as our physical system of interest tells us what we intend to focus on, which

184_notes:defining_current

Anonymous (anonymous@undisclosed.example.com) — 2021-02-23T20:31:47+00:00

Defining Current In the last few pages of notes, we have talked about how the surface charges are arranged to create a constant electric field in the wire. This electric field is responsible for pushing the electrons through the wire from one side of the battery to the other - creating a flow of electrons, which we called $$i=\frac{\# electrons}{second}$$$n$$A$$v_{avg}$$$i=nAv_{avg}$$$n$$8.4 \cdot 10^{28} \frac{electrons}{m^3}$$A$$v$$$\frac{\# electrons}{s}=\frac{\# electrons}{m^3}*m^2*\frac{m}…

184_notes:dipole_sup

Anonymous (anonymous@undisclosed.example.com) — 2020-08-17T17:29:24+00:00

Dipole Superposition Example In the last page of notes, you read about how superposition applies in general for electric field and electric potential. These notes will go into more detail about how to calculate the electric field using superposition for the specific example of an electric dipole. (We are showing this example of electric field, rather than electric potential, because the $r$$\vec{E}_{net}$$\vec{E}_{+}$$\vec{E}_{-}$$$\vec{E}_{net}=\vec{E}_{+}+\vec{E}_{-}$$$$ E_{+}=\frac{1}{4\pi\e…

184_notes:dist_charges

Anonymous (anonymous@undisclosed.example.com) — 2021-02-13T19:26:26+00:00

Distributions of Charges Over the last set of notes, we have talked about how we use superposition to find the electric field or electric potential from a line of charge, how you set up the dQ and the $\vec{r}$, and how to use those steps in a specific example. For this class, we will expect you to be able to set up these kinds of integrals for a line a charge (1D), but we will not go into the mathematics for 2D or 3D distributions of charge. Even though we won't go into the integral set up or …

184_notes:dq

Anonymous (anonymous@undisclosed.example.com) — 2021-05-26T13:36:37+00:00

Sections 15.1-15.2 in Matter and Interactions (4th edition) dQ and the $\vec{r}$ We've talked about how we can calculate the electric field or electric potential for any shape of charge by breaking it into little pieces of charge, calculating the field from each piece of charge, then adding all of those little fields together (using $\vec{r}$$dx$$dy$$\lambda$$\frac{C}{m}$$\lambda$$$\lambda=\frac{Q_{tot}}{L_{tot}}$$$$dQ=\lambda dl= \lambda dx = \lambda dy$$$C=\frac{C}{m}*m$$dA$$\sigma$$\frac{C}…

184_notes:e_and_b

Anonymous (anonymous@undisclosed.example.com) — 2018-04-06T16:29:22+00:00

Relating Electric and Magnetic Fields Thus far in this course, we have considered the electric and magnetic fields completely separately, either only looking at the effects of an electric field by itself or a magnetic field by itself. However, there are many real-world contexts where a charge may be moving in a magnetic field and also near other charges. This means the charge would feel both an electric force and a magnetic force. Through Newton's second law ($\vec{F}_{net}=\vec{F}_1+\vec{F}_2+

184_notes:e_b_summary

Anonymous (anonymous@undisclosed.example.com) — 2021-06-16T22:36:41+00:00

Summary of Electricity and Magnetism (thus far) So far in this course we have primarily talked about static electric fields (Weeks 1 - 3), how static electric fields apply to circuits (Weeks 4 - 6), and static magnetic fields (Weeks 7 - 9). We have primarily been treating these phenomena as independent (i.e. only looking at the electric field or only looking at the magnetic field). However, as you may have guessed, these ideas are not completely separate. For example, let's say that you had a p…

184_notes:e_flux

Anonymous (anonymous@undisclosed.example.com) — 2021-05-29T19:08:06+00:00

Section 21.2 in Matter and Interactions (4th edition) Electric Flux and Area Vectors In general, any sort of flux is how much of something goes through an area. For example, we could think of a kid's bubble wand in terms of the air flux (from you blowing) through the circle (with the bubble solution in it). If you wanted to make bigger bubbles or make many more bubbles, you could do two things: increase the air flow or get a bubble wand with a bigger circle. Both of these actions (increasing t…

184_notes:e_parallel_plates

Anonymous (anonymous@undisclosed.example.com) — 2017-08-10T14:49:51+00:00

Electric Field between Parallel Plates We can find the electric field between the plates using Gauss's Law (just like you did in Project 5). We know that for two parallel plates, there is an electric field in the middle that points directly from the positive plate to the negative plate (except near the edges where the field bends slightly out). Outside of the plates, the electric field is zero because the contributions from the negative and positive plates will cancel. $$\int \vec{E} \cdot \vec…

184_notes:efieldvector

Anonymous (anonymous@undisclosed.example.com) — 2017-06-15T22:47:48+00:00

Calculation for Electric Field Vectors We can follow a very similar process for Points B-D as we did to calculate the electric field for Point A. For Point B, we start with: $$\vec{E_B} = \frac{1}{4 \pi\epsilon_0}\frac{Q}{r_B^2} \hat{r_B}$$ Now $\vec{r_B}$ has the same length as $\vec{r_A}$ but points only in the +x direction $$\vec{r_B}=\langle d,0,0 \rangle$$ So the magnitude and unit vector are given by: $$r_B=|\vec{r_B}|=\sqrt{r_{Bx}^2+r_{By}^2+r_{Bz}^2}=\sqrt{d^2+0^2+0^2}$$$$r_B = d$$$$\h…

184_notes:eflux_curved

Anonymous (anonymous@undisclosed.example.com) — 2021-06-01T15:29:43+00:00

Section 21.3 from Matter and Interaction (4th edition) Electric Flux through Curved Surfaces We talked already about how to calculate the electric flux through a flat surface and through an enclosed cube for a constant electric field. But what happens if the field is not constant? Or what if the surface is no longer flat? These notes will show how we modify the electric flux equation to account for varying fields and curved surfaces. $d\vec{A}$$dA$$\hat{n}$$$d\vec{A}=dA \hat{n}$$$d\vec{A}$$d\…

184_notes:electric_field

Anonymous (anonymous@undisclosed.example.com) — 2021-07-06T17:28:59+00:00

Chapters 13-16 (and 18-19) in Matter and Interactions (4th editions) The Electric Field What has driven the development of all the physics and mathematics we have done is one simple observation: Matter is charged. That is, matter has a property called charge, which stems from the fact that it is made up of charged particles: electrons and protons. This simple observation leads to a fundamental idea in electromagnetism: $$\vec{E} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\hat{r}.$$$\vec{r}$$$…

184_notes:energy_review

Anonymous (anonymous@undisclosed.example.com) — 2023-08-22T14:51:40+00:00

Sections ??? of Matter and Interactions (4th edition) Review of Energy In addition to forces and accelerations, energy is an alternative tool we can use to understand how systems behave. We will spend a lot of time on energy, and the closely related idea of electric potential, in EMP-Cubed. This page contains brief reminders of the key ideas about energy from your mechanics course; for more details refer to the readings from Physics 183.$E$$K$$U$$U_g$$1.602 \times 10^{-19}$$K \rightarrow U$$…

184_notes:examples

Anonymous (anonymous@undisclosed.example.com) — 2018-04-11T19:28:05+00:00

Examples 184 * call it something Week 2 * Find the total charge for a mole of electrons * Interactions Between Charged and Neutral Objects * Attempting to Charge Insulators by Induction * Electric Field from a Negative Point Charge * Electric Potential from a Positively Charged Balloon * Electric Potential from a Negatively Charged Balloon * Plotting Electric Potential with Wolfram Alpha Week 3 * Superposition with Three Point Charges * Plotting Potential for Multiple Ch…

184_notes:extra_sup

Anonymous (anonymous@undisclosed.example.com) — 2018-01-19T00:50:24+00:00

Dipole Superposition Example In the last page of notes, you read about how superposition applies in general for electric field and electric potential. These notes will go into more detail about how to calculate the electric field using superposition for the specific example of an electric dipole. (We are showing this example of electric field, rather than electric potential, because the $\vec{E}_{net}$$\vec{E}_{+}$$\vec{E}_{-}$$$\vec{E}_{net}=\vec{E}_{+}+\vec{E}_{-}$$$$ E_{+}=\frac{1}{4\pi\epsi…

184_notes:extra_words

Anonymous (anonymous@undisclosed.example.com) — 2018-01-27T18:43:13+00:00

Conventional Current vs Electron Current Electron Current Before, we defined the electron current as the number of electrons passing through a point per second. Because the electron current is made up of negative charges, the electron current will always flow opposite to the electric field. (This is a more general rule that you may remember from before - electrons will always move opposite to the direction of the electric field.) We will use a lower-case $$i=\frac{\# electrons}{second}$$$n$$A$…

184_notes:fab_physics

Anonymous (anonymous@undisclosed.example.com) — 2019-01-11T04:42:29+00:00

Space Shield Fab Physics Week 1 Before we go to Mars we need to test safety features such as the ability to stop harmful radiation. You are part of a team that is designing a “force” field that will deflect alpha particles. You need to create a design that will stop alpha particles that are shooting directly at a group of astronauts who are creating a habitat on the moon as a test run. The alpha particles are traveling with a speed of 1.28 * $10^{+07}$$$U_i+K_i=U_f+K_f$$$U_i=0$$K_i$$U_f$$K_f =0…

184_notes:fall_notes_layout

Anonymous (anonymous@undisclosed.example.com) — 2019-01-03T23:31:38+00:00

184 Notes - Fall (2018) Review Materials Review of Key Concepts from Mechanics * Math Review * Defining a System * 3 Fundamental Principles of Mechanics * Using Python * Common Commands in Python Week 1 Modeling a Single Point Charge * Electric Charge * Charge and Matter * Charging and Discharging * Electric Field * Electric Potential * Relating Electric Field and Electric Potential Week 2 Superposition and Modeling Two Point Charges * Electric Force * E…

184_notes:force_review

Anonymous (anonymous@undisclosed.example.com) — 2023-08-18T14:05:52+00:00

Sections ??? of Matter and Interactions (4th edition) Review of Forces One of the core ideas from your mechanics course is that objects accelerate in response to forces. We will apply the same ideas in this course to understand electricity and magnetism, so it's important that you remember how forces work. This page is a brief review of the key ideas about forces from mechanics. If your recollection of any of these concepts isn't clear, you may want to go back and review the details in the …

184_notes:future_additions

Anonymous (anonymous@undisclosed.example.com) — 2017-10-02T16:27:06+00:00

Future Additions/Corrections to Curriculum General Things * Add video examples * Add subtitles to videos - this may be happening already * Add “Handy Hints” - i.e. assumptions are italisized and underlined - chances are you will use these in your projects

184_notes:gauss_ex

Anonymous (anonymous@undisclosed.example.com) — 2021-06-04T00:36:02+00:00

Section 21.3 from Matter and Interactions (4th edition) Putting Gauss's Law Together At this point, we have talked about how to find the electric flux through flat surfaces and through curved surfaces as well how to find the enclosed charge using charge density. These notes will go through two examples of how we find the electric field at a single point using electric flux, enclosed charge and symmetry arguments (Gauss's Law). You should notice many similarities between the steps that we use f…

184_notes:gauss_motive

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T13:42:51+00:00

Motivation for Gauss's Law Last week, we learned about Ampere's Law, which was a cool shortcut for finding magnetic fields in highly symmetric situations. This week we will talk about a similar short for finding electric fields in symmetric situations, called Gauss's Law. While Gauss's Law has many similar features to Ampere's Law, there are a couple of key differences. First, we will be talking about enclosing a charge, rather than a current (since we are returning to a discussion about electr…

184_notes:getting_started

Anonymous (anonymous@undisclosed.example.com) — 2024-08-20T16:17:54+00:00

Getting Started Part of what you'll be working on this semester is learning how to plan and organize your work through complex problem solving with a group. Keeping your work organized is important for several reasons - 1) making sure you're not missing any critical information from the problems, 2) making sure that everyone in the group understands each step along the way, and 3) making sure that you understand what happened in the problem when you look back at your work (e.g. for homework or …

184_notes:glowscript

Anonymous (anonymous@undisclosed.example.com) — 2025-01-19T21:09:44+00:00

Getting Started with Glowscript Glowscript encounters some problems when using Safari. Please use Google Chrome as your browser when using Glowscript. If you encounter any issues with Glowscript, log out and close your browser, then log back in and try again.

184_notes:gradient

Anonymous (anonymous@undisclosed.example.com) — 2021-02-23T20:18:38+00:00

Surface Charge Gradients In the previous page of notes, we showed that there must be some charges along the surface of a wire and they must be arranged in a gradient. We call these charges along the surface of the wire surface charges. The surface charges create an electric field in the wire, which then pushes electrons through the wire to create a current. In this page of notes, we will dig a little deeper into what a gradient of surface charges actually is and how we represent that gradient o…

184_notes:i_b_force

Anonymous (anonymous@undisclosed.example.com) — 2021-07-13T11:58:12+00:00

Section 20.2 in Matter and Interactions (4th edition) Magnetic Force on a Current Carrying Wire Since we deal with currents on a daily basis in all of electronics, it is particularly important and relevant to consider the force on a current-carrying wire. These notes will step through how get from the magnetic force on a single moving charge to the force on a current. $$d\vec{F}= dq \vec{v}\times\vec{B}$$$dq$$\vec{v}$$\frac{m}{s}$$\vec{B}$$T$$\vec{v}=\frac{d\vec{l}}{dt}$$$d\vec{F}= dq \frac{d…

184_notes:i_thru

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T13:29:06+00:00

Section 21.6 in Matter and Interactions (4th edition) Current through a loop Now that we have the left side of the equation, the next step is to talk about the right side of Ampere's law - namely the $\mu_0 I_{enc}$ bit. For an Amperian loop that is outside of a single wire, this part is actually rather simple, but it starts to become more complicated when we consider loops inside the wire. As we said before, if the wire is a bit thick, we can investigate what happens to the magnetic field ins…

184_notes:if

Anonymous (anonymous@undisclosed.example.com) — 2022-05-07T01:21:49+00:00

Coding: "If Statements" Lecture Video Sometimes, we only want the computer to execute code in specific cases. For instance, only divide if the denominator is nonzero. How can the computer decide if the denominator is nonzero? One way is by using an if statement:

184_notes:ind_graphs

Anonymous (anonymous@undisclosed.example.com) — 2022-12-07T14:43:07+00:00

Induction Graphs In these notes, we will examine a few examples of changing magnetic fluxes and associated induced voltages. Recall from the previous notes that these are related by Faraday's Law which says: $$V_{ind} = -\frac{d\Phi_b}{dt}$$ This is saying that the induced current is the $V_{ind}$$V_{ind}$$V_{ind} = 0$$\Phi_B$$t = 0$$t = 5$$\Phi_B(t)$$V_{ind}$$t = 5$$t = 10$$\Phi_B(t)$$V_{ind}$$\Phi_B(t)$$$ \Phi_B(t)= \begin{cases} 2t & \text{if } 0

184_notes:ind_i

Anonymous (anonymous@undisclosed.example.com) — 2022-11-15T16:21:31+00:00

Sections 22.1-22.3 in Matter and Interactions (4th edition) The Curly Electric Field and Induced Current Now that we have talked about the changing magnetic flux part of Faraday's law, we should go back to the right hand side and talk about the curly electric field (the $\int \vec{E}_{nc} \bullet d\vec{l}$$\vec{E}$$\vec{E}_{nc}$$V_{ind}$$V_{ind}$$\int \vec{E}_{nc} \bullet d\vec{l}$$\frac{V}{m}\cdot m= V$$$V_{ind}=\int \vec{E}_{nc} \bullet d\vec{l}$$$\int \vec{E}_{c} \bullet d\vec{l}$$$V_{ind}=…

184_notes:induced_current

Anonymous (anonymous@undisclosed.example.com) — 2021-11-12T23:15:39+00:00

Finding the Induced Current Direction So far, we've been talking about the different pieces of Faraday's Law - namely how a changing magnetic flux will create an induced current. In this page of notes, we will outline the steps that we need to take to determine the direction of the induced current, which are based off of Faraday's Law itself:$$V_{ind} = -\frac{d \Phi_B}{dt}$$$\vec{v}$$d\vec{A}$$d\vec{A}$$d\vec{A}$$d\vec{A}$$d\vec{A}$$\vec{B}$$d\vec{A}$$$\Phi_B = \int \vec{B} \bullet d\vec{A} = …

184_notes:induction_graphs

Anonymous (anonymous@undisclosed.example.com) — 2022-11-15T16:31:22+00:00

Flux Graphs

184_notes:kirchoffs_rules

Anonymous (anonymous@undisclosed.example.com) — 2022-02-21T21:52:13+00:00

Using Loop and Node Rules to Solve Circuits So far this week, we have talked about how to deal with circuit elements that are in series and in parallel. We can use these rules for resistance, along with Ohm's law, to figure out the current and voltage at every point in the circuit. However, how do you solve circuits that are neither in series or parallel? Or when there are multiple voltage sources? For circuits that don't follow the series/parallel rules, we can always go back to the $V_1$$V_2$…

184_notes:level_up_sol

Anonymous (anonymous@undisclosed.example.com) — 2020-10-26T21:41:05+00:00

Level Up Answers Level 0 Circuit A: $$R_{eq}=R_1+R_2+R_3= 9 Ω$$ $$V_3>V_2>V_1$$ $$I_1=I_2=I_3$$ Circuit B: $$C_{eq}=(\frac{1}{C_1}+ \frac{1}{C_2}+ \frac{1}{C_3})^{-1}= 2.3 mF$$ $$Q_{1}=Q_{2}=Q_{3}$$ $$V_1>V_2>V_3$$ Circuit C: $$C_{eq}=C_1+C_2+C_3 = 21 mF$$ $$V_{1}=V_{2}=V_{3}$$ $$Q_3>Q_2>Q_1$$ Circuit D: $$R_{eq}=(\frac{1}{R_1}+ \frac{1}{R_2}+ \frac{1}{R_3})^{-1}= 0.92 Ω$$ $$V_{1}=V_{2}=V_{3}$$ $$I_1>I_2>I_3$$ Level 1 Circuit A: $R_{eq}= 350 Ω$ Circuit B: $R_{eq}= 400 Ω$ Circuit C: $C_{…

184_notes:lightning

Anonymous (anonymous@undisclosed.example.com) — 2021-02-09T19:20:54+00:00

As taken from the National Weather Service Website ().

184_notes:line_fields

Anonymous (anonymous@undisclosed.example.com) — 2021-02-13T18:58:12+00:00

Sections 15.1-15.2 in Matter and Interactions (4th edition) Electric Field and Potential for Lines of Charge In the previous notes, we talked about how to add fields using superposition, which can be greatly aided by the use of a computer (especially if there are many charges). We can also do a similar process for a line of charge analytically (using ideas from calculus) rather than using code. We will also talk about how these ideas ideas extend to large distributions of charge (including 2D …

184_notes:linecharge

Anonymous (anonymous@undisclosed.example.com) — 2021-07-22T18:17:18+00:00

Sections 15.1-15.2 in Matter and Interactions (4th edition) Lines of Charge Examples Now that we have the ideas behind how to construct the electric or potential field for distributions or lines of charges, we can put all of these pieces together to find the fields in specific examples. We will outline the steps for two examples in these notes, and you will get to try them out for yourselves in class and in the homework.$L$$Q$$A$$d$$x=0$$+x$$-x$$-\frac{L}{2}$$\frac{L}{2}$$$\vec{E}=\int\frac{1}…

184_notes:lists

Anonymous (anonymous@undisclosed.example.com) — 2022-05-07T01:20:19+00:00

Coding: Lists We often need a way to represent a group of objects or values in code. Python makes this easy with lists. A list gives a name to a collection of any Python objects. You can think of a list like an excel spreadsheet, it has many rows (each representing an object), and each row has several columns (representing the attributes of the object).

184_notes:loop

Anonymous (anonymous@undisclosed.example.com) — 2022-04-04T12:46:53+00:00

Section 21.6 in Matter and Interactions (4th edition) Magnetic field along a closed loop For the context of our explanation, we will use a long straight wire with a current $I$ running through it as our example. We'll start by talking about a thin wire and eventually build up to talking about a thick wire. In this class, we will also make the typical $$\oint \vec{B} \bullet d\vec{l} = \mu_0 I_{enc}$$$\oint \vec{B} \bullet d\vec{l}$$\vec{B}\bullet d\vec{l}$$$\oint \vec{B} \bullet d\vec{l}.$$$R$…

184_notes:loops

Anonymous (anonymous@undisclosed.example.com) — 2022-05-07T01:19:21+00:00

Coding: Loops You can think of coding as writing instructions for a computer to follow. Let's say I want my computer to print out each of the numbers from 1 to 100. In Python, printing a number is easy: print(1) This will print the number 1. Printing all the numbers from 1 to 100 is a little more challenging though. Here's one way:

184_notes:mag_interaction

Anonymous (anonymous@undisclosed.example.com) — 2021-03-18T16:16:38+00:00

Magnetic Interaction This week we are going to start to talk about a new kind of interaction: the magnetic interaction. Pieces of this section may feel familiar from when we talked about the electric interaction, while other pieces will feel new. As we will talk about in a couple of weeks, the electric field $m$$\vec{B}$$32*10^{-6}$$0.005 T$$1-5$$1T=10,000G$

184_notes:magnetic_field

Anonymous (anonymous@undisclosed.example.com) — 2021-07-06T17:31:12+00:00

Chapters 17 and 20 of Matter and Interactions (4th edition) The Magnetic Field When charges are at rest, they generate an electric field. Set that charge into motion and you have a new observation: moving charges generate magnetic field. This field, originally thought to be completely different from the electric field, has its own form of interaction. Like the electric field, the magnetic field also permeates all of space, and it gets weaker as you are further from the source. The magnetic fie…

184_notes:magnetic_interaction

Anonymous (anonymous@undisclosed.example.com) — 2018-02-23T03:27:16+00:00

184_notes:math_review

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T19:30:42+00:00

Math Review The following mathematical ideas are important to understand and to be able to use as we will rely on them fairly heavily in this course. These notes will provide a review of these ideas with links to more thorough resources if you feel like you need more information about a topic. $number \cdot 10^{exponent}$$x=5,430,000 m$$x=5.43 \cdot 10^{6} m$$y=.00000458m$$y=4.58 \cdot 10^{-6}m$$y=4.58 \mu m$$10^9$$10^6$$10^3$$10^0$$10^{-2}$$10^{-3}$$\mu$$10^{-6}$$10^{-9}$$10^{-12}$$$ \mathbf{a…

184_notes:maxwells_eq

Anonymous (anonymous@undisclosed.example.com) — 2021-07-06T17:53:59+00:00

Section 22.4 and 23.1 in Matter and Interactions (4th edition) Putting Together Maxwell's Equations Now that we have added the final addition to Ampere's Law, we have a set of four equations that fully describe the sources of electric and magnetic fields from charges. Together, these four equations are called $$\int \vec{E} \bullet d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$$$$-\int \vec{E} \bullet d\vec{l} = \frac{d\Phi_B}{dt}$$$$\int \vec{B}\bullet d\vec{A} = 0 $$$$\int \vec{B} \bullet d\vec{l} =…

184_notes:metals

Anonymous (anonymous@undisclosed.example.com) — 2025-02-14T14:40:19+00:00

Lightbulbs'R'Us Warehouse Metals Metal Symbol $\mu$ (units: $\frac{m/s}{V/m}$) $n$ (units: $\frac{\# electrons}{m^3}$) Nichrome Ni-Cr-Fe $7.0 \times 10^{-5}$ $9 \times 10^{28}$ Silver Ag $5.7 \times 10^{-3}$ $5.9 \times 10^{28}$ Tungsten W $1.2 \times 10^{-4}$ $6.3 \times 10^{28}$ Aluminum Al $1.3 \times 10^{-3}$ $1.8 \times 10^{29}$ Copper Cu $4.5 \times 10^{-3}$ $8.4 \times 10^{28}$ Gold Au $4.3 \times 10^{-3}$ $6.1 \times 10^{28}$

184_notes:motiv_amp_law

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T13:28:15+00:00

Sections 21.5 and 21.6 in Matter and Interactions (4th edition) Motivating Ampere's Law So far in this course, we have talked about the sources of electric fields, how electric fields are applied to circuits, and the sources of magnetic fields. Over the next two weeks, we are going to talk about two mathematical shortcuts for calculating the electric and magnetic fields: Ampere's Law and Gauss's Law. In both Ampere's Law and Gauss's Law, we will require that either the magnetic field (for Ampe…

184_notes:motiv_b_force

Anonymous (anonymous@undisclosed.example.com) — 2022-03-16T20:44:56+00:00

Sections 2.1-2.3 and 5.2 in Matter and Interactions (4th edition) Magnetic Forces in the Real World In this set of notes we will be defining the push or pull produced by a magnetic field (maybe not surprisingly) as the magnetic force. We will continue to look at the most simple case - the force from a magnetic field on a single moving charge, before moving on to consider more complicated situations like a current carrying wire. It turns out that the most complicated case with regards to magnet…

184_notes:motiv_movingq

Anonymous (anonymous@undisclosed.example.com) — 2021-02-16T19:45:55+00:00

Modeling Moving Charges Thus far in class, we've have spent a lot of time modeling stationary charges and their interactions, including electric force, electric field, electric potential energy, and electric potential. We've discussed these ideas in the context of point charges, lines of charge, and distributions (or volumes) of charge. Now, we will shift our focus to modeling moving charges - which has incredibly important applications for how electricity and circuits work. Using what we know …

184_notes:moving_charges_make_magnetic_fields

Anonymous (anonymous@undisclosed.example.com) — 2018-02-23T03:30:41+00:00

Section 17.3 in Matter and Interactions (4th edition) Moving Charges Make Magnetic Fields Just like we did with electric fields, we will start with magnetic fields by looking at the simplest source: a single moving point charge. When we are talking about this moving charge and the corresponding magnetic field, there are intuitive qualities that we want to make sure our mathematical model includes: (1) the farther away the observation point is from the moving charge, the smaller that we expect …

184_notes:moving_q

Anonymous (anonymous@undisclosed.example.com) — 2021-07-05T21:51:13+00:00

184_notes:patterns_fields

Anonymous (anonymous@undisclosed.example.com) — 2021-02-13T19:30:41+00:00

Patterns in the Electric Field In the last page of notes, we talked about two different examples of distributions of charges (both spheres and cylinders) for both conducting materials and insulating materials. It is worth highlighting some common features and patterns of fields for these larger shapes.

184_notes:pc_efield

Anonymous (anonymous@undisclosed.example.com) — 2021-05-26T13:39:02+00:00

Sections 13.1 - 13.4 of Matter and Interactions (4th edition) Electric Field of a Point Charge In electricity and magnetism, the idea of a field becomes a very powerful concept that allows us to explain and predict phenomena that we would not otherwise be able to (like how visible light, infrared, and x-rays work). In this course, we will start by talking about the electric field, which is produced by charge(s) and decreases with the distance away from the charge(s). These notes will explain t…

184_notes:pc_energy

Anonymous (anonymous@undisclosed.example.com) — 2024-01-22T22:26:30+00:00

Sections 6.9 and 16.1 - 16.3 in Matter and Interactions (4th edition) Electric Potential Energy As you read about in the electric force, we noted that the electric force is a conservative force. This means we can define a potential energy - electric potential energy$$\Delta U = -\int_i^f\vec{F}\bullet d\vec{r}$$$U_{elec}$$$\Delta U_{elec}= -\int_i^f\vec{F}_{elec}\bullet d\vec{r}$$$r$$r_i$$r_f$$q_1$$q_2$$q_1$$q_2$$$\Delta U_{elec} = U_f-U_i= -\int_i^f\vec{F}_{elec}\bullet d\vec{r}$$$q_1$$q_2$$r…

184_notes:pc_force

Anonymous (anonymous@undisclosed.example.com) — 2021-01-27T15:57:48+00:00

Sections 3.7, 13.2 - 13.3 , and 13.6 of Matter and Interactions (4th edition) Electric Force Last week, you have read about the electric field and electric potential that is created by a single point charge. Here you will read about what happens when you have two point charges that are near each other. $\vec{E}_{net}$$$\vec{F}_{net \rightarrow q}=q*\vec{E}_{net}$$$net \rightarrow q$$y=3m$$y=5m$$$\vec{F}_{net \rightarrow q}=q\vec{E}_{net}$$$q$$\vec{F}_{q}$$\vec{E}_{net}$$q_{+}$$q_{-}$$q_+$$q_+$…

184_notes:pc_potential

Anonymous (anonymous@undisclosed.example.com) — 2021-01-26T19:17:05+00:00

Some of Sections 16.3, 16.5, and 16.7 in Matter and Interactions (4th edition) Electric Potential of a Point Charge In the last page of notes, you read that the electric field is a vector field that any charge will produce. A charge will also produce a scalar field called the $$V=\frac{1}{4\pi\epsilon_0}\frac{q}{r}$$$\frac{1}{4\pi\epsilon_0}$$\epsilon_0 = 8.85\cdot10^{-12} \frac{C^2}{N m^2}$$$r=|\vec{r}|=|\vec{r_p}-\vec{r_q}|$$$V = 4 \text{ V}$$V = 4$$1.4\cdot10^{-7} \text{ V}$$V=\frac{1}{4\p…

184_notes:pc_vefu

Anonymous (anonymous@undisclosed.example.com) — 2021-01-29T20:48:22+00:00

Relationships between Force, Field, Potential, and Energy You may have noticed in reading about electric field, electric potential, electric force, and electric potential energy that these quantities are very similar and follow very similar patterns. These notes will summarize the relationships between the four quantities, highlight their similarities and differences, and revisit the relationships between the four quantities for point charges.$\hat{r}$$-\hat{r}$$q$$q$

184_notes:perm_mag

Anonymous (anonymous@undisclosed.example.com) — 2021-07-05T21:52:06+00:00

Section 17.11 and 17.12 in Matter and Interactions (4th edition) Permanent Magnets In addition to moving charges, another source of magnetic fields that we are going to talk about are permanent magnets. These are the magnets that probably you have seen, have experience with, and already know about (i.e. refrigerator magnets, the Earth, the traditional U-shaped magnets, etc.). While these are much more frequently used in everyday life, permanent magnets are actually quite complicated and are an…

184_notes:permanent_magnets

Anonymous (anonymous@undisclosed.example.com) — 2018-02-23T03:44:54+00:00

184_notes:python_syntax

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T19:31:46+00:00

Common Commands and Tips for Python In this class, we are often going to use VPython to create computational models, which will serve as a powerful tool to help us create visualizations and apply the ideas in this course to more real-world contexts. Below are some of the common Python commands that we will use in this course and some coding tips compiled by previous EMP-Cubed students. (Note: we do not expect you to have any coding experience prior to this course, and we will not expect you to …

184_notes:q_b_force

Anonymous (anonymous@undisclosed.example.com) — 2021-06-08T18:43:37+00:00

Section 20.1 in Matter and Interactions (4th edition) Magnetic Force on Moving Charges We'll start thinking about the magnetic force in terms of the simplest case: a single moving charge through an external magnetic field. The source of the external magnetic field could be another moving charge, a current, a bar magnet or any combination of those. Most of the time though, we will concern ourselves with how the charge interacts with the field (whatever it may be) and we will not care as much ab…

184_notes:q_enc

Anonymous (anonymous@undisclosed.example.com) — 2021-06-04T00:34:22+00:00

Section 21.1 from Matter and Interactions (4th edition) Enclosed Charge One of the coolest, yet strangest, features of Gauss's Law is that the electric flux through the imagined Gaussian surface is related to the total amount of charge inside the surface (the $dQ$$\lambda$$C/m$$\sigma$$C/m^2$$\rho$$C/m^3$$$\lambda=\frac{Q_{tot}}{L_{tot}}\:\:\:\:\:\:\:\:\:\:\:\: \sigma=\frac{Q_{tot}}{A_{tot}}\:\:\:\:\:\:\:\:\:\:\:\: \rho=\frac{Q_{tot}}{V_{tot}}$$$$Q=\lambda L=\frac{Q_{tot}}{L_{tot}}L\:\:\:\:\:\…

184_notes:q_in_wires

Anonymous (anonymous@undisclosed.example.com) — 2021-06-08T00:38:10+00:00

Sections 17.1, 17.5, and 18.1-18.5 in Matter and Interactions (4th edition) Surface Charges around a Circuit We have already talked about how to model a battery as a separation of charges. However, if we connect the two ends of the battery with a conducting wire, what happens to the charge distribution in the wire? Using $$\vec{F}_{e^-}=q_{e^-}\vec{E}$$

184_notes:q_path

Anonymous (anonymous@undisclosed.example.com) — 2021-07-07T14:37:41+00:00

Section 20.1 in Matter and Interactions (4th edition) Path of a Charge through a Magnetic Field We just talked about the force that a moving charge feels when it travels through a magnetic field. So now the question remains: what happens to the charge when it feels this force? Since the magnetic force is perpendicular to the velocity of the charge, $-\hat{x}$$-\hat{z}$$-\hat{y}$$$\Delta \vec{p} = \vec{p}_f - \vec{p}_i = \vec{F}_{net,avg} \Delta t$$$\vec{p}=m\vec{v}$$$\vec{p}_f = \vec{F}_{net,…

184_notes:r_energy

Anonymous (anonymous@undisclosed.example.com) — 2021-06-14T23:41:53+00:00

Sections 18.3, 18.8-18.10, and 19.4 in Matter and Interactions (4th edition) Energy around the Circuit One of the consequences of adding a resistor in the circuit (with higher electron speed and a higher electric field) is that a large energy transfer$$\Delta E_{sys}=0$$$$\Delta E_{bat}+\Delta E_{wires}+\Delta E_{filament}+\Delta E_{surr}=0$$$$\Delta V_1+\Delta V_2+\Delta V_3+...=0$$$$P=\frac{\Delta U}{\Delta t}=\frac{dU}{dt}$$$W=\frac{J}{s}$$1-5$$=1-5 \cdot 10^6$$$\frac{C}{s}*V=\frac{J}{s}$$$…

184_notes:r_parallel

Anonymous (anonymous@undisclosed.example.com) — 2021-06-28T23:42:23+00:00

Sections 19.2 and 19.3 in Matter and Interactions (4th edition) Resistors in Parallel Another way to combine resistors is in parallel. This means that there are at least two “parallel” paths that start from the same potential and end at the same potential, $I$$I_1$$I_2$$R_1$$R_2$$$I_{bat}=I_1+I_2$$$$+|\Delta V_{bat}| - |\Delta V_1| = 0$$$$|\Delta V_{bat}|=|\Delta V_1|$$$$+|\Delta V_{bat}| - |\Delta V_2| = 0$$$$|\Delta V_{bat}|=|\Delta V_2|$$$R_1$$R_2$$$+|\Delta V_1|-|\Delta V_2| = 0$$$$|\Delta…

184_notes:r_series

Anonymous (anonymous@undisclosed.example.com) — 2021-06-28T23:17:58+00:00

Sections 19.2 and 19.3 in Matter and Interactions (4th edition) Resistors in Series Up until now, we have talked about resistors from a very microscopic point of view and have introduced the idea of resistance, which helps us talk about resistors from a more macroscopic perspective. This week will be continuing to consider circuits from a macro-view and thinking about what happens when we combine multiple circuit elements in one circuit. These notes will focus on a particular way to combine re…

184_notes:relating_e

Anonymous (anonymous@undisclosed.example.com) — 2021-06-29T17:03:45+00:00

Sections 22.1-22.3 in Matter and Interactions (4th edition) Putting All of Faraday's Law Together To summarize what we just learned, we found that a changing magnetic flux will create a curly electric field. This means that we now have two source of electric fields - one being the static charges (that we talked about at the beginning of the semester) and the second being changing magnetic fields. $$\int \vec{E}_{nc} \bullet d\vec{l}= - \frac{d \Phi_B}{dt}$$$$V_{ind}=I_{ind}R=-\frac{d \Phi_B}{d…

184_notes:relating_ev

Anonymous (anonymous@undisclosed.example.com) — 2020-08-17T16:37:09+00:00

Relating Electric Potential to Electric Field At this point you may have noticed some similarities between electric field and electric potential: * They use the same constant * They both relate to the amount of charge you have * They both get smaller when you increase the distance from the charge$\frac{1}{r^2}$$\frac{1}{r}$$$V=\frac{1}{4\pi\epsilon_0}\frac{q}{r}$$$$\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2} \hat{r}$$$\hat{r}$$$\vec{E}=-\frac{dV}{dr}\hat{r}$$$$\vec{E}=-\frac{dV}{dx}\ha…

184_notes:resistivity

Anonymous (anonymous@undisclosed.example.com) — 2021-02-27T04:07:03+00:00

Section 19.2 in Matter and Interactions (4th edition) Resistors and Conductivity So far we have been approaching circuits from a very microscopic picture, including talking about the surface charges, electron currents, and electric fields in the wires. However, the surface charges, electric fields, and individual electrons are extremely difficult to measure. Instead, it often much more useful to think about circuits in terms of macroscopic properties, which are much easier to measure (i.e., co…

184_notes:resistors

Anonymous (anonymous@undisclosed.example.com) — 2021-03-04T19:46:23+00:00

Sections 18.3, 18.8-18.10, and 19.4 in Matter and Interactions (4th edition) Resistors in Circuits To this point, we have talked about what happens inside a wire when connected to two ends of battery - both in the steady state current situation and in the initial transient when the circuit is first connected. We found a few important conclusions about the circuit in $v_{avg}$$$i_{thin}=i_{thick}$$$$n A_{thin} u E_{thin}= n A_{thick} u E_{thick}$$$$E_{thin}=\frac{A_{thick}}{A_{thin}}E_{thick}$$…

184_notes:rhr

Anonymous (anonymous@undisclosed.example.com) — 2022-11-06T16:08:21+00:00

The Right Hand Rule The Right Hand Rule is a handy tool to figure out the directions of vectors in a cross product. There are multiple ways to do the Right Hand Rule, we will present two methods below (though there are more). Feel free to use whatever method makes the most sense to you. For the following methods, we will be using a generic cross product: $$\vec{A} \times \vec{B} = \vec{C}$$$\vec{A}$$\vec{B}$$\vec{C}$$\vec{C}$$\vec{A}$$\vec{B}$$\vec{C}$$\vec{B}$$-\vec{v}$

184_notes:right_hand_rule

Anonymous (anonymous@undisclosed.example.com) — 2018-02-23T14:54:26+00:00

184_notes:short_name

Anonymous (anonymous@undisclosed.example.com) — 2018-02-09T16:28:17+00:00

Title of the Page Goes Here Introduce all the things Section titles have one less equal sign Add some words here and all that jazz Don't forget the syntax link above that has all the info on how to write the things.

184_notes:spring_notes_layout

Anonymous (anonymous@undisclosed.example.com) — 2021-08-18T17:27:34+00:00

184 Notes - Spring 2019 Review Materials Review of Key Concepts from Mechanics * Math Review * Defining a System * 3 Fundamental Principles of Mechanics * Using Python * Common Commands in Python Week 1 Modeling a Single Point Charge * Electric Charge * Electric Field * Electric Potential * Relating Electric Field and Electric Potential Week 2 Superposition and Modeling Two Point Charges * Charge and Matter * Charging and Discharging * Electric Force * …

184_notes:start_s18

Anonymous (anonymous@undisclosed.example.com) — 2018-01-09T22:28:20+00:00

Notes - Spring 2018 Review Topics Review of Key Concepts from Mechanics * Math Review * Defining a System * 3 Fundamental Principles of Mechanics * Using Python Week 1 Modeling a Single Point Charge * Electric Charge * Charge and Matter * Charging and Discharging * Electric Field * Electric Potential

184_notes:start

Anonymous (anonymous@undisclosed.example.com) — 2023-09-15T17:40:15+00:00

184 Notes - Fall 2023 Review Materials - Key Concepts from Calculus and Mechanics * Defining a System * 3 Fundamental Principles of Mechanics Week 1 - Charges, Electric Field & Electric Potential * Math Review * Electric Charge * Electric Field * Electric Potential * Relating Electric Field and Electric Potential Week 2 - Charges & Superposition * Charge and Matter * Charging and Discharging * Superposition * Dipole Superposition Example * Using Python * Co…

184_notes:steady_state

Anonymous (anonymous@undisclosed.example.com) — 2017-09-20T20:06:04+00:00

Connecting a Circuit: Before Steady State So far, we have talked about how to model batteries and electron current for a steady state current (meaning the wire has been connected for some time). We found that there must be a constant, continuous electric field along the wire that comes from the wire's surface charges to push the electron current through the wire to the battery. But what happens before the steady state current is reached? These notes will go into detail about how a steady curren…

184_notes:superposition_b

Anonymous (anonymous@undisclosed.example.com) — 2021-06-10T01:37:15+00:00

Superposition Superposition is central to understanding of all E&M fields and governs how all of these fields add up. That is, magnetic field vectors superpose just as you might expect. This means that if you have two moving charges, the magnetic field at any given point is given by the vector addition of the magnetic field due to one of the moving charges $$\vec{B}_{total}=\vec{B}_1+\vec{B}_2$$$$\vec{B}_{total}=\vec{B}_1+\vec{B}_2+\vec{B}_3+\vec{B}_4+...$$

184_notes:superposition

Anonymous (anonymous@undisclosed.example.com) — 2021-05-26T13:41:22+00:00

Sections 13.5 and 13.6 in Matter and Interactions (4th edition) Superposition Over the last two weeks, you have read about the electric field and electric potential that is created by a single point charge. While a single point charge is definitely the simplest case, most charged objects that you will run into are not single point charges. These notes will talk about the electric field and electric potential due to multiple charges - starting with the next most complicated case: two point char…

184_notes:superposition2

Anonymous (anonymous@undisclosed.example.com) — 2018-02-23T03:43:16+00:00

184_notes:symmetry

Anonymous (anonymous@undisclosed.example.com) — 2021-07-06T17:51:20+00:00

Chapter 21 in Matter and Interactions (4th edition) Symmetry and Mathematical Tools One of the important aspects of electromagnetism is understanding the patterns of the electric and magnetic fields that the charges and current produce. These patterns can often suggest a symmetry $$\Phi_E = \oint \vec{E} \bullet d\vec{A} = \dfrac{q_{enc}}{\varepsilon_0}$$$$\oint \vec{E} \bullet d\vec{A} = E \oint dA = \dfrac{q_{enc}}{\varepsilon_0}$$$q$$r$$$\oint \vec{E} \cdot d\vec{A} = \dfrac{q_{enc}}{\varep…

184_notes:three_principles

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T19:31:13+00:00

The Three Fundamental Principles of Mechanics A major focus of introductory mechanics is understanding three fundamental principles of how objects interact (though they may have been called by different names): the momentum principle, the energy principle, and the angular momentum principle. These principles are central to the study of physics broadly, not simply mechanics; they are $$\Delta \vec{p}_{sys} = \vec{F}_{ext} \Delta t$$$$\Delta \vec{p}_{sys} = 0 \longrightarrow \vec{p}_{sys,i} = \ve…

184_notes:troubleshooting

Anonymous (anonymous@undisclosed.example.com) — 2022-05-06T22:06:53+00:00

Coding: When it all Goes Wrong A programming project isn't complete without an error that seems impossible to fix. Glowscript's error messages can be vague. If you find yourself completely lost in a coding project, the best bet is usually to take a step back. Go back to your pseudocode and comments, and compare them to the code you have written. Is each line doing exactly what it should be? Be particularly careful with loops and if statements, and consider the location of each line within a loo…

184_notes:using_python

Anonymous (anonymous@undisclosed.example.com) — 2020-08-24T19:31:28+00:00

Making Models with VPython Computers and computational modeling provide a powerful (and almost necessary) tool in modern scientific research and engineering work. While analytic (i.e., paper and pencil) solutions do exist for some problems, computational modeling allows you to create 3D visualizations, incorporate more complex behavior, model millions of particles at the same time, analyze massive amounts of data, or simply solve repetitive calculations. In addition to solving analytic problems…

184_notes:what_happens

Anonymous (anonymous@undisclosed.example.com) — 2021-06-17T15:24:22+00:00

Section 22.1 and 22.2 in Matter and Interactions (4th edition) What happens when Magnetic Fields Change? Thus far in this course, we have considered the electric and magnetic fields completely separately, either only looking at the effects of an electric field by itself or a magnetic field by itself. However, there are many real-world contexts where a charge may be moving in a magnetic field and also near other charges. This means the charge would feel both an $\vec{F}_{net}=\vec{F}_1+\vec{F}_…