Question

A field of $100V{m}^{-1}$ is directed at ${30}^o$ to positive x-axis. Find $(V_A-V_B)$ if $OA=2m$ and $OB=4m$.

• A. $100(\sqrt{3}-2)V$
• B. $-100(2+\sqrt{3})V$
• C. $100(2-\sqrt{3})V$
• D. $200(2+\sqrt{3})V$

Answer 1

The correct option is B $-100(2+\sqrt{3})V$

A field of $=100v/m$ directed $={30}^0$

$V_A-V_B=?$

$OA=2m$

$OB=4m$

Exaplanation

$\overline{E}=(100\cos {30}^0\hat{i}+100\sin {30}^0\hat{j})$

$\overline{F}=50\sqrt{3}\hat{i}+50\hat{j}$

$A=(2m,0)$

$B=(0,4m)$

$V_A-V_B=-{\int }_B^A\overline{E}.d\overline{r}$

$={\int }_{(-2,0)}^{(0,4)}50\sqrt{3}dx+50dy$

$={[50\sqrt{3}x+50y]}_{(2,0)}^{(0,4)}$

$=-100(2-\sqrt{3})$