Question

A uniform electric field having strength $\overrightarrow{E}$ is existing in x-y plane as shown in figure. Find the potential difference between origin O and A $(d,d,0)$:

• A. $-Ed(\cos \theta +\sin \theta )$
• B. $Ed(\cos \theta -\sin \theta )$
• C. $\sqrt{2}Ed$
• D. none of these

Answer 1

The correct option is A $-Ed(\cos \theta +\sin \theta )$

Here , $\overrightarrow{E}=E\cos \theta \hat{i}+E\sin \theta \hat{j}$
Potential,$V=-{\int }_{(0,0,0)}^{(d,d,0)}\overrightarrow{E}.\overrightarrow{dr}$

$=-{\int }_{(0,0,0)}^{(d,d,0)}(E\cos \theta \hat{i}+E\sin \theta \hat{j}).(dx\hat{i}+dy\hat{j})=-[E\cos \theta {\int }_0^{d}dx+E\sin \theta {\int }_0^{d}dy]$

$=-Ed(\cos \theta +\sin \theta )$