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 different $V_0-V_A$ is :

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

Answer 1

Answer: (C)

$-100\sqrt{3}V$

$d_1=AOcos{30}^{\circ }=2\sqrt{3}/2=\sqrt{3}m$

$d_2=BOsin{30}^{\circ }=4\times \frac{1}{2}=2m$

$V_A-V_0=E{d}_1=100\sqrt{3}V$

or $V_0-V_A=-100\sqrt{3}V$

$V_A-V_B=E(d_1+d_2)=100(\sqrt{3}+2)V$

or $V_B-V_A=100(\sqrt{3}+2)V$