184_notes:induced_current

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184_notes:induced_current [2021/04/08 19:15] – [Step 6: Determining the direction of $I_{ind}$] dmcpadden184_notes:induced_current [2021/11/12 23:15] (current) – [Step 1.) Draw a picture of your situation] stumptyl
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 We will use the example of a bar magnet moving away from a wire coil to highlight these steps and to show how you can use a table to keep track of your work. While the specifics of the table will change depending on the context, the structure and steps will work no matter what problem you are solving. So to get started you should make a table like the one shown to the right with 8 columns. The first column will be for a picture/diagram of your situation, the second will be for the B-field direction, the third will be for the dA direction, the fourth will be for your initial magnetic flux, the fifth will be for the final magnetic flux, the sixth will be the change in magnetic flux, the seventh will be for your induced voltage, and the eighth will be for your induced current.  We will use the example of a bar magnet moving away from a wire coil to highlight these steps and to show how you can use a table to keep track of your work. While the specifics of the table will change depending on the context, the structure and steps will work no matter what problem you are solving. So to get started you should make a table like the one shown to the right with 8 columns. The first column will be for a picture/diagram of your situation, the second will be for the B-field direction, the third will be for the dA direction, the fourth will be for your initial magnetic flux, the fifth will be for the final magnetic flux, the sixth will be the change in magnetic flux, the seventh will be for your induced voltage, and the eighth will be for your induced current. 
  
-[{{184_notes:inducedcurrent_blank.png?600|This is the table used for predicting the directional of the induced current.  }}]+[{{184_notes:inductionchart_updated_11_12_2021.png?600|This is the table used for predicting the directional of the induced current.  }}]
  
 +This video will walk you through an example of how to use this table or you can read about it in the notes below.
  
 +{{youtube>Qlg0Iu1Do94?large}}
 +\\
 +**NOTE: In this chart there is a mistake in the chart being used: The variables "V" and "I" are not vectors. Please make a note of this when watching the video to ensure there is no confusion.**
 ==== Right Hand Rule Steps ==== ==== Right Hand Rule Steps ====
  
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 Before anything, you should start with a picture of your situation. We'll draw this in the first column of the table. For our example, we'll have a bar magnet that is moving away from a set of coils. In the picture, we have marked the coils, the orientation of the magnet (which side is north/south), and which way the magnet is moving (marked with the velocity $\vec{v}$ arrow). Before anything, you should start with a picture of your situation. We'll draw this in the first column of the table. For our example, we'll have a bar magnet that is moving away from a set of coils. In the picture, we have marked the coils, the orientation of the magnet (which side is north/south), and which way the magnet is moving (marked with the velocity $\vec{v}$ arrow).
  
-[{{184_notes:ic_scenario.png?440| Step 1: First make a diagram of the particular situation include the coil, magnet, and relevant directions. +[{{184_notes:inductionchart_updated_11_12_2021.png?440| Step 1: First make a diagram of the particular situation include the coil, magnet, and relevant directions. 
  }}]  }}]
  
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 Next we need to determine the direction of the magnetic field through the relevant area. For this situation, the relevant area is going to be our coils, so we are particularly interested in the direction of the B-field through the coils. Remember for a bar magnet, the magnetic field should point out from the north side of the magnet, wrap around, and point into the south side of the magnet. Since our coil is next to the south side of the magnet, this means the magnetic field inside the coil will mostly be pointing to the left (in towards the south side of the magnet). So in the second column we will put an arrow to the left. Next we need to determine the direction of the magnetic field through the relevant area. For this situation, the relevant area is going to be our coils, so we are particularly interested in the direction of the B-field through the coils. Remember for a bar magnet, the magnetic field should point out from the north side of the magnet, wrap around, and point into the south side of the magnet. Since our coil is next to the south side of the magnet, this means the magnetic field inside the coil will mostly be pointing to the left (in towards the south side of the magnet). So in the second column we will put an arrow to the left.
  
-[{{184_notes:ic_bfield.png?440| Step 2: isolates the direction of the magnetic field and now places that corresponding vector into the chart. }}]+[{{184_notes:inductionchart_partb.png?440| Step 2: isolates the direction of the magnetic field and now places that corresponding vector into the chart. }}]
  
  
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 Remember that the $d\vec{A}$ is perpendicular to the cross section area of the coils. Meaning, that you can think of the $d\vec{A}$ as pointing "out of” the coil. For our set up, this means that $d\vec{A}$ could point either to the left or right (-x or +x direction). It doesn't matter which way you pick, as long as the $d\vec{A}$ is perpendicular to the area. For this example, we'll pick the $d\vec{A}$ to point to the left, so we draw an arrow in the third column that points to the left. Remember that the $d\vec{A}$ is perpendicular to the cross section area of the coils. Meaning, that you can think of the $d\vec{A}$ as pointing "out of” the coil. For our set up, this means that $d\vec{A}$ could point either to the left or right (-x or +x direction). It doesn't matter which way you pick, as long as the $d\vec{A}$ is perpendicular to the area. For this example, we'll pick the $d\vec{A}$ to point to the left, so we draw an arrow in the third column that points to the left.
  
-[{{184_notes:ic_da.png?440| Step 3: Pick a direction for dA that points perpendicular to the coil. In this example, we pick  dA to be to the left.  }}] +[{{184_notes:inductionchart_partc.png?440| Step 3: Pick a direction for dA that points perpendicular to the coil. In this example, we pick  dA to be to the left.  }}] 
  
 ====Step 4.) $\Phi_{B,i}$, $\Phi_{B,f}$ and $\frac{d\Phi_{B}}{dt}$==== ====Step 4.) $\Phi_{B,i}$, $\Phi_{B,f}$ and $\frac{d\Phi_{B}}{dt}$====
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 The magnitude of the flux will depend on the size of the B-field and area at that particular time. For example if your bar magnet is close to your loop, you'd expect a big flux since the magnetic field is stronger closer to the magnet. The sign of the flux will be determined by the dot product of $\vec{B}$ and $d\vec{A}$. Remember we can simplify the flux equation by saying: The magnitude of the flux will depend on the size of the B-field and area at that particular time. For example if your bar magnet is close to your loop, you'd expect a big flux since the magnetic field is stronger closer to the magnet. The sign of the flux will be determined by the dot product of $\vec{B}$ and $d\vec{A}$. Remember we can simplify the flux equation by saying:
-$$\Phi_B = \int \vec{B} \bullet d\vec{A} = B *dA *cos(\theta)$$+$$\Phi_B = \int \vec{B} \bullet d\vec{A} = \int B *dA *cos(\theta)$$
 So if $\theta$ is between $0^\circ-90^\circ$, then we know the flux will be positive. If $\theta$ is between $90^\circ-180^\circ$, then the flux will be negative. So let's go through this for our example.  So if $\theta$ is between $0^\circ-90^\circ$, then we know the flux will be positive. If $\theta$ is between $90^\circ-180^\circ$, then the flux will be negative. So let's go through this for our example. 
  
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 In our case, this means we'd be taking a small positive number minus a big positive number. This will result in a //negative// change in flux. (If it helps, you can assign numbers to help you think through this. For example, we could take $2-10 = -8$.) So we write down in the sixth column that the change in flux is negative. In our case, this means we'd be taking a small positive number minus a big positive number. This will result in a //negative// change in flux. (If it helps, you can assign numbers to help you think through this. For example, we could take $2-10 = -8$.) So we write down in the sixth column that the change in flux is negative.
  
-[{{184_notes:ic_flux.png+[{{184_notes:inductionchart_partd.png
 ?440|Step 4: Determine the sign of the change in flux based on the initial and final flux for the situation.  }}] ?440|Step 4: Determine the sign of the change in flux based on the initial and final flux for the situation.  }}]
  
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 For our example, the change in flux was negative. So we write down "positive" for the $V_{ind}$ column. For our example, the change in flux was negative. So we write down "positive" for the $V_{ind}$ column.
  
-[{{184_notes:ic_vinduced.png+[{{184_notes:inductionchart_parte.png
 ?440|Step 5: The sign of the V-induced is the **opposite** of the change in flux.  }}] ?440|Step 5: The sign of the V-induced is the **opposite** of the change in flux.  }}]
  
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 For our example, we found that $V_{ind}$ was positive. So this means that we would stick our thumb in the -x direction (pointing to the left) and then curl our fingers around in a circle. You should find the the current would go into the page at the top of the coil and would come back out of the page at the bottom of the coil. Just because it's often hard to draw the current direction in 3D, we often will just notate where on the coil the current is into/out of the page. For our example, we found that $V_{ind}$ was positive. So this means that we would stick our thumb in the -x direction (pointing to the left) and then curl our fingers around in a circle. You should find the the current would go into the page at the top of the coil and would come back out of the page at the bottom of the coil. Just because it's often hard to draw the current direction in 3D, we often will just notate where on the coil the current is into/out of the page.
  
-[{{184_notes:inductionrhr.png+[{{184_notes:inductionchart_partf.png
 ?440|Step 6: Find the direction of the induced current based on the right hand rule. }}] ?440|Step 6: Find the direction of the induced current based on the right hand rule. }}]
  
 The right hand rule for determining the induced current direction is definitely more complicated than our previous right hand rules; however, this table helps break the process down into manageable chunks. We definitely recommend writing out each step in this way - otherwise it is easy to miss a step or a negative sign, which will throw off your final result. The right hand rule for determining the induced current direction is definitely more complicated than our previous right hand rules; however, this table helps break the process down into manageable chunks. We definitely recommend writing out each step in this way - otherwise it is easy to miss a step or a negative sign, which will throw off your final result.
  • 184_notes/induced_current.1617909351.txt.gz
  • Last modified: 2021/04/08 19:15
  • by dmcpadden