Question
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....$V$
✓
Answer
Potential difference between any two points in an electric field is given by,
${\mathrm{d} \mathrm{V}=-\vec{E} \cdot \overrightarrow{d x}}$
${\int_{V_{O}}^{V_{A}} d V=-\int_{0}^{2} 30 x^{2} d x}$
${V_{A}-V_{O}=-\left[10 x^{3}\right]_{0}^{2}=-80\, \mathrm{J} / \mathrm{C}}$
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