Question

Assume that an electric field $\overrightarrow{E}=30x^2\hat{i}$ exists in space. Then the potential difference $V_A-V_0$, where $V_0$ is the potential at the origin and $V_A$ the potential at $x=2\text{m}$, is :

• A. $-120\text{J}$
• B. $80\text{J}$
• C. $120\text{J}$
• D. $-80\text{J}$

Answer 1

The correct option is D $-80\text{J}$

Given: $\overrightarrow{E}=30x^2\hat{i}$

Potential difference between any two points in an electric field is given by, $dV=-\overrightarrow{E}.\overrightarrow{dx}$

$\Rightarrow V_A-V_0=-{\int }_0^A{E}_{x}dx$
$=-{\int }_0^{2}30x^{2}dx$
$=-30{\left[\frac{x^3}{3}\right]}_0^2$
$=-30\frac{2^3}{3}=-80\text{V}$

Hence, option $\left(C\right)$ is correct.