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Potential Energy - External Viewpoint

A uniform ele...

Question

A uniform electric field of $20$ NC $^{- 1}$ exists along the x-axis in space. The potential difference V $_{B} -$ V $_{A}$ for the point A $=$ $(4 m, 2 m)$ and B $=$ $(6 m, 5 m)$ is:

20

\sqrt{13}

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- 40 V

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zero V

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none of the above

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Solution

The correct option is B $- 40 V$
Here, $\to E = 20^i \Rightarrow E_{x} = 20$
Potential difference , $V_{B} - V_{A} = - \int_{A}^{B} E d r = - \int_{4}^{6} E_{x} d x = - 20 \int_{4}^{6} d x = - 20 (6 - 4) = - 40 V$

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