Question

An electric field $\overrightarrow{E}=(25\hat{i}+30\hat{j})N{C}^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x=2m,y=2m$ is

• A. $-110J$
• B. $-140J$
• C. $-130J$
• D. $-120J$

Answer 1

The correct option is A $-110J$

Potential difference between two points $\Delta V=$ work done per unit charge$=\frac{\int \overrightarrow{F}.\overrightarrow{dr}}{q}=\frac{\int q\overrightarrow{E}.\overrightarrow{dr}}{q}$

$\Delta V=-\int \overrightarrow{E}.\overrightarrow{dr}$ ...(i)

$E=25\hat{i}+30\hat{j}$ and coordinates of given point $\overrightarrow{r}=2\hat{i}+2\hat{j}\overrightarrow{dr}=dx\hat{i}+dy\hat{j}$ substituting values in equation (i)

$\Delta V=-{\int }_{\overrightarrow{0}}^{\overrightarrow{r}}25\hat{i}+30\hat{j}.dx\hat{i}+dy\hat{j}$

$\Delta V=-{\int }_0^{2}25dx+{\int }_0^{2}30dy$

$=[25x{]}_0^2+[[30y{]}_0^2$

$=50+60=-110V$

$V-V_{origin}=-110J$ given $V_{origin}=0$

$V=-110J$ hence correct answer is option A