Question

A uniform electric field of $100V{m}^{-1}$ is directed at ${30}^{\circ }$ with the positive x-axis as shown in Fig. $OA=2m$ and $OB=4m$. The potential difference $V_B-V_A$ is :

• A. $-100[2+\sqrt{3}]V$
• B. $100[2+\sqrt{3}]V$
• C. $100[2-\sqrt{3}]V$
• D. $-100[2-\sqrt{3}]V$

Answer 1

The correct option is A $-100[2+\sqrt{3}]V$

Since, We know that
$V=-\int \overrightarrow{E}.\overrightarrow{dr}$

and since Electric field is uniform we can directly write it in form
$V=-\overrightarrow{E.}\overrightarrow{r_{AB}}$

Hence
$V=-\left(100\right(\left(\sqrt{3}/2\right)\hat{i}+\left(1/2\right)\hat{j}).(2\hat{i}+4\hat{j}\left)\right)$

which gives
$V=-100(2+\sqrt{3})$