Question

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

• A. - 110 V
• B. - 140 V
• C. - 120 V
• D. - 130 V

Answer 1

The correct option is A - 110 V

A electric field $\underset{E}{⟶}(25\hat{i}+30\hat{j})N/C$

$X=2m$

$y=2m$

$E=25\hat{i}+30\hat{j}$

$\frac{dV}{dx}=-E\Rightarrow \Delta V=-{\int }_1^2\overline{E}.d\overline{v}$

$d\overline{v}=dx\hat{i}+dy\hat{j}$

$V_2-V_1=-{\int }_1^2(2\delta \hat{i}+30\hat{j})(dx\hat{i}+dy\hat{j})$

$=-{\int }_1^2(-25dx+30dy)$

$V_2=0$,

$=-25{\left[x\right]}_0^2-30{\left[y\right]}_0^2$

$V_2=(-25-30)\times 2=-110V$