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  4. Assume that an electric field vecE=30 x2 hati exists in space. Then the potential difference VA-VO' where VO is the potential at the origin and VA the potential at x=2 m is

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

JEE MainJEE Main 2014Electrostatic Potential and Capacitance

Solution:

$dV=-\vec{E} \cdot \overline{d x} $
$\int\limits_{V_{0}}^{V_{A}} d V=-\int\limits_{0}^{2} 30 x^{2} d x$
$V_{A}-V_{O}=-\left[10 x^{3}\right]_{0}^{2}=-80 \,J$