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| 184_notes:examples:week2_electric_field_negative_point [2018/02/03 21:15] – tallpaul | 184_notes:examples:week2_electric_field_negative_point [2021/05/19 15:11] (current) – schram45 |
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| | [[184_notes:pc_efield|Return to Electric Field]] |
| ==== Example: Electric Field from a Negative Point Charge ===== | ==== Example: Electric Field from a Negative Point Charge ===== |
| Suppose we have a negative charge −Q. What is the magnitude of the electric field at a point P, which is a distance R from the charge? Draw the electric field vector on a diagram to show the direction of the electric field at P. | Suppose we have a negative charge −Q. What is the magnitude of the electric field at a point P, which is a distance R from the charge? Draw the electric field vector on a diagram to show the direction of the electric field at P. |
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| ===Representations=== | ===Representations=== |
| {{ 184_notes:2_potential_negative_point.png?150 |Negative Point Charge -Q, and Point P}} | [{{ 184_notes:2_potential_negative_point.png?150 |Negative Point Charge -Q, and Point P}}] |
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| | <WRAP TIP> |
| | ===Assumptions=== |
| | * Constant charge: Makes charge in electric field equation not dependent on time or space as no information is given in problem suggesting so. |
| | * Charge is not moving: This makes our separation vector fixed in time as a moving charge would have a changing separation vector with time. |
| | </WRAP> |
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| ===Goal=== | ===Goal=== |
| This leaves us to find the unit vector ˆr. The first thing to do would be to draw in the separation vector, →r−Q→P. This vector points from the charge −Q to Point P since P is where we want to find the electric field (our observation location). We need to define a set of coordinate axes. We could pick the normal x- and y-axes, but this would make writing the →r and ˆr more difficult because there would be both x- and y-components to the separation vector (since it points in some diagonal direction). | This leaves us to find the unit vector ˆr. The first thing to do would be to draw in the separation vector, →r−Q→P. This vector points from the charge −Q to Point P since P is where we want to find the electric field (our observation location). We need to define a set of coordinate axes. We could pick the normal x- and y-axes, but this would make writing the →r and ˆr more difficult because there would be both x- and y-components to the separation vector (since it points in some diagonal direction). |
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| {{ 184_notes:2_electric_field_negative_point_s_direction.png?300 |s-direction drawn in}} | [{{ 184_notes:2_electric_field_negative_point_s_direction.png?300 |s-direction drawn in}}] |
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| Instead, we'll pick a coordinate direction that falls along the same axis as the separation vector, →r−Q→P. Since this is a coordinate direction that we're naming, let's call this the ˆs direction. That means that →r−Q→P points in the ˆs direction, so ˆr=ˆs. Plugging this into our electric field equation gives: | Instead, we'll pick a coordinate direction that falls along the same axis as the separation vector, →r−Q→P. Since this is a coordinate direction that we're naming, let's call this the ˆs direction. That means that →r−Q→P points in the ˆs direction, so ˆr=ˆs. Plugging this into our electric field equation gives: |
| This gives the magnitude of the electric field as |→E|=14πϵ0QR2
| This gives the magnitude of the electric field as |→E|=14πϵ0QR2
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| with the direction is given by −ˆs. The electric field at P therefore points from P to the point charge. You'll find this to be true for all negative charge - **the electric field points towards negative charges**. A diagram indicating the direction of the electric field is shown below. | with the direction is given by −ˆs. The electric field at P therefore points from P to the point charge. You'll find this to be true for all negative charge - **the electric field points towards negative charges**. A diagram indicating the direction of the electric field is shown below. |
| {{ 184_notes:2_electric_field_negative_point_solution.png?150 |Charge Distribution Induced From Two Sides, Solution}} | [{{ 184_notes:2_electric_field_negative_point_solution.png?150 |Charge Distribution Induced From Two Sides, Solution}}] |