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Q.

Assume that an electric field $\overset{⇀}{E} = 30 x^{2} \hat{j}$ exists in space. Then the potential difference $V_{A} - V_{0}$ where $V_{0}$ is the potential at the origin and $V_{A}$ the potential at $x = 2 m$ is:

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a

120J/C

b

-120J/C

c

-80J/C

d

80J/C

answer is C.

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Detailed Solution

Potential difference between any two points in an electric filed is given by,

$d V = - \vec{E} . \vec{d x} \int_{V_{0}}^{V_{A}} d V = - \int_{0}^{0} 30 x^{2} d x V_{A} - V_{0} = - {[10 x^{3}]}_{0}^{2} = - 80 J / C$

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