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 $x=2 \mathrm{~m}$ is
(2014 Main)
(a) $120 \mathrm{~J}$
(b) $-120 \mathrm{~J}$
(c) $-80 \mathrm{~J}$
(d) $80 \mathrm{~J}$
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Answer:
Correct Answer: 9. (c)
Solution:
- As we know, potential difference $V_{A}-V_{O}$ is
$$ \begin{aligned} d V & =-E d x \\ \Rightarrow \quad \int_{V_{o}}^{V_{A}} d V & =-\int_{0}^{2} 30 x^{2} d x \\ V_{A}-V_{O} & =-30 \times \frac{x^{3}}{3} \\ & =-10 \times\left[2^{3}-(0)^{3}\right] \\ & =-10 \times 8=-80 \mathrm{~J} \end{aligned} $$
