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Assume that an electric field $E = 30 x^{2} \hat{i}$ exists in space. Then, the potential difference $V_{A} - V_{o},$ where
V_o is the potential at the origin and V_A is the potential at x = 2 m, is

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120 V

$-$ 120 V

$-$ 80 V

80 V

answer is C.

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Detailed Solution

We have, potential difference, $V_{A} - V_{o} = - \int_{o}^{A} E_{x} dx$

Potential difference, $V_{A} - V_{o} = - \int_{0}^{2} 30 x^{2} dx$

$= - 30 (\frac{2^{3}}{3}) = - 80 V$

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