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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 // | The figure below summarizes the // | ||
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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 Force and Electric Potential Energy describe an **interaction** - They require two charged objects or two systems of charged objects; you cannot describe the force or energy of just one charge (this is why we have electric potential and electric field). | * Electric Force and Electric Potential Energy describe an **interaction** - They require two charged objects or two systems of charged objects; you cannot describe the force or energy of just one charge (this is why we have electric potential and electric field). | ||
* 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. | ||
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=== Example for Point Charges === | === 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). | ||
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* 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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