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Q.

A uniform electric field having a magnitude $E_{0}$ and direction along the positive X-axis exists. If the potential V is zero at $x = 0,$ then its value at $X = + x$ will be

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a

$V (x) = + x^{2} E_{0}$

b

$V (x) = + x E_{0}$

c

$V (x) = - x E_{0}$

answer is B.

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Detailed Solution

$∵ E = - \frac{dV}{dX} \Rightarrow V_{x} = - E_{0} \int_{0}^{x} dx = - {xE}_{0}$

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A uniform electric field having a magnitude E0 and direction along the positive X-axis exists. If the potential V is zero at x=0, then its value at X=+x will be