Assume that an electric field vec E = 30{x^2}hat{i} exists in space. Then potential difference V_A-V

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2. Electric Potential and Capacitance

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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....$V$

A

$-120$

B

$-80$

C

$80$

D

$120$

(JEE MAIN-2014)

Solution

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

${\mathrm{d} \mathrm{V}=-\vec{E} \cdot \overrightarrow{d x}}$

${\int_{V_{O}}^{V_{A}} d V=-\int_{0}^{2} 30 x^{2} d x}$

${V_{A}-V_{O}=-\left[10 x^{3}\right]_{0}^{2}=-80\, \mathrm{J} / \mathrm{C}}$

Standard 12

Physics

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