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

• A. 120 J
• B. -120 J
• C. -80 J
• D. 80 J

Answer 1

Answer: (C)

-80 J

Answer 2

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