Question

The potential at the origin is zero due to electric field $\overline{E}=20\hat{i}+30\hat{j}N{C}^{-1}$ . The potential at point $P(2m,2m)$ is:

• A. $100V$
• B. $-100V$
• C. $-140V$
• D. $140V$

Answer 1

The correct option is C $-140V$

We know $v_{r_1}-v_{r_2}=-{\int }_{r_2}^{r_1}Edr$
$v_{x_0}-v_{x_2}=-{\int }_2^{0}20dr$
$\Rightarrow v_{x_2}=-40$
$v_{y_0}-v_{y_2}=-{\int }_2^{0}30dr$
$v_{y_2}=-60dr$
$totalv=v_{x_2}+v_{y_2}=-100v$