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Electric Field

If V0 be th...

Question

If $V_{0}$ be the potential at origin in an electric field $\to E = E_{x}^j + E_{y}^j$ , then the potential at point $P (x, y)$ is

A

V_{0} + x E_{x} + y E_{y}

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B

V_{0} + x E_{x} - y E_{y}

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C

V_{0} - x E_{x} - y E_{y}

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D

\sqrt{(x^{2} + y^{2})} \sqrt{E_{x}^{2} + E_{y}^{2}} - V_{0}

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Solution

The correct option is D $V_{0} - x E_{x} - y E_{y}$
$P (x, y)$
$V_{0}$ =potential at origin.
Potential at $P = V_{0} - V_{P}$
$V = E \cdot d$ where $E$ =Electric field, $d$ =Distance.
$V_{p} = x \cdot E_{x} + y \cdot E_{y}$
$V_{0} - V_{p} = V_{0} - (x E_{x} + y E_{y})$
$= V_{0} - x E_{x} - y E_{y}$

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