Relationships Between Force, Field, Energy, Potential Video Lessons

Concept

# Problem: 1. Assume the electric field E in some region is uniform: it is the same at all points. Specifically, E has a magnitude of 5 V/m and points in the +x direction. What can you then say about the behavior of the electric potential a) in the x-direction and b) in the y-direction? Explain your answers. 2. Suppose you have a uniform Electric field with a magnitude of 5 V/m in the +x direction. (i) What can you say about the potential difference between two points separated by a distance of 2 m along the x-axis? (ii) What can you say about the potential difference between two points separated by a distance of 3 m along the y-axis? (iii) Is your answer to this question consistent with the answer to question 1?

###### FREE Expert Solution

(1)

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{∆}\mathbf{V}}{\mathbf{∆}\mathbf{x}}}$

For uniform E, ΔV varies linearly. That is, V is a linear function dependent on the position, x.

Electric field points from higher potential to lower potential.

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###### Problem Details

1. Assume the electric field E in some region is uniform: it is the same at all points. Specifically, E has a magnitude of 5 V/m and points in the +x direction. What can you then say about the behavior of the electric potential a) in the x-direction and b) in the y-direction? Explain your answers.

2. Suppose you have a uniform Electric field with a magnitude of 5 V/m in the +x direction.

(i) What can you say about the potential difference between two points separated by a distance of 2 m along the x-axis?

(ii) What can you say about the potential difference between two points separated by a distance of 3 m along the y-axis?