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| 184_notes:pc_vefu [2018/05/24 15:13] – curdemma | 184_notes:pc_vefu [2021/01/29 20:48] (current) – [General Relationships] bartonmo | ||
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| ===== Relationships between Force, Field, Potential, and Energy ===== | ===== Relationships between Force, Field, Potential, and Energy ===== | ||
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| ==== General Relationships ==== | ==== General Relationships ==== | ||
| - | The figure below summarizes the //__general__// relationships between the four quantities. **These relationships are always true**. It does not matter if you have a point charge, a sphere of charge, a cylinder of charge, or a random blob of charge - these relationships will always be true. | + | The figure below summarizes the //general// relationships between the four quantities. **These relationships are always true**. It does not matter if you have a point charge, a sphere of charge, a cylinder of charge, or a random blob of charge - these relationships will always be true. |
| + | [{{ 184_notes: | ||
| - | {{ 184_notes: | ||
| A couple of things to notice about these relationships: | A couple of things to notice about these relationships: | ||
| * Electric Field and Electric Force are **vectors** - They have a magnitude and direction at every location in space. | * Electric Field and Electric Force are **vectors** - They have a magnitude and direction at every location in space. | ||
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| * Electric Field and Electric Potential describe a **single** charge or system of charges - They require one charged object or a system of charged objects and describe the vector and scalar fields around that object. | * Electric Field and Electric Potential describe a **single** charge or system of charges - They require one charged object or a system of charged objects and describe the vector and scalar fields around that object. | ||
| - | === Example for Point Charges === | + | |
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| + | ==== Example for Point Charges | ||
| Over the past two weeks, we have been modeling point charges. Using the general relationships above, we found: | Over the past two weeks, we have been modeling point charges. Using the general relationships above, we found: | ||
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| **Note: these equations are only true for point charges**. They are not true for other types or shapes of charges. However, we see very similar patterns for the point charges. | **Note: these equations are only true for point charges**. They are not true for other types or shapes of charges. However, we see very similar patterns for the point charges. | ||
| * Electric Field and Electric Force are both **vectors** - They both point in the $\hat{r}$ direction (or $-\hat{r}$ direction depending on the kinds of the charge). | * Electric Field and Electric Force are both **vectors** - They both point in the $\hat{r}$ direction (or $-\hat{r}$ direction depending on the kinds of the charge). | ||
| * Electric Potential and Electric Potential Energy are both **scalars** - There is no direction associated with them. | * Electric Potential and Electric Potential Energy are both **scalars** - There is no direction associated with them. | ||
| - | * Electric Force and Electric Energy describe an **interaction** - There must be (at the minimum) two point charges, which is why there are two q's in the equation | + | * Electric Force and Electric Energy describe an **interaction** - There must be (at the minimum) two point charges, which is why there are two $q$'s in the equation |
| - | * Electric Field and Electric Potential describe a **single** charge - There is only one q in each equation. | + | * Electric Field and Electric Potential describe a **single** charge - There is only one $q$ in each equation. |
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| + | [{{184_notes: | ||