Assume an electric field $E = 30 x \hat i$ exists in space. If $V_0$ is the potential at the origin and $V_A$ is the potential at $x = 2 m$, then the potential difference $V_A- V_0$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -60 V
Given electric field: $\vec{E} = 30x\,\hat{i}$
Relation between electric field and potential:
$E_x = -\frac{dV}{dx}$
$\Rightarrow \frac{dV}{dx} = -30x$
Integrating from $x = 0$ to $x = 2$:
$V_A - V_0 = \int_{0}^{2} \frac{dV}{dx} \, dx = \int_{0}^{2} (-30x)\,dx$
$V_A - V_0 = -30 \left[\frac{x^2}{2}\right]_0^2 = -30 \left(\frac{4}{2}\right)$
$V_A - V_0 = -60\,V$
Potential difference $V_A - V_0 = -60\,V$