Electrostatics 2 Question 9
9. Assume that an electric field $\mathbf{E}=30 x^{2} \hat{\mathbf{i}}$ 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
(2014 Main)
(a) $120 J$
(b) $-120 J$
(c) $-80 J$
(d) $80 J$
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Answer:
Correct Answer: 9. (a)
Solution:
- As we know, potential difference $V _A-V _O$ is
$$ \begin{aligned} d V & =-E d x \\ \Rightarrow \quad \int _{V _o}^{V _A} d V & =-\int _0^{2} 30 x^{2} d x \\ V _A-V _O & =-30 \times \frac{x^{3}}{3} \\ & =-10 \times\left[2^{3}-(0)^{3}\right] \\ & =-10 \times 8=-80 J \end{aligned} $$
