Question

$E=20\hat{i}+30\hat{j}$ exists in space. If the potential at the origin is taken to be zero, find the potential at $P(3,2)$.

• A. $-150V$
• B. $-100V$
• C. $+150V$
• D. $-120V$

Answer 1

The correct option is D $-120V$

Electric field in x-y plane $\overrightarrow{E}=-\hat{i}\frac{d{V}_x}{dx}-\hat{j}\frac{d{V}_y}{dy}$
and given $\overrightarrow{E}=20\hat{i}+30\hat{j}$
$\frac{d{V}_x}{dx}=-20$ and $\frac{d{V}_y}{dy}=-30$
integraing, $V_x={\int }_0^3(-20)dx=-60$ and $V_y={\int }_0^2(-30)dy=-60$
As the potential is a scalar quatity so the potential $V_P=V_x+V_y=-60-60=-120V$