Assume an electric field \( \vec{E} = 30\,x\,\hat{\imath} \) exists in space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 2\,\mathrm{m} \), then the potential difference \( V_A - V_0 \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( -60\,\mathrm{V} \)
The potential difference between two points is the negative line integral of the field, \( V_A - V_0 = -\int E\,dx \). The field here depends on \( x \), so it has to be integrated.
\( \displaystyle V_A - V_0 = -\int_{0}^{2} 30\,x\,dx = -30\left[\frac{x^{2}}{2}\right]_{0}^{2} \)
\( \displaystyle V_A - V_0 = -30\times\frac{4}{2} = -60\,\mathrm{V} \)