Question

Two point charges $4\mu C$ and $9\mu C$are separated by a distance of 50 cm. The potential at the point between them where the field has zero strength is

• A. $4.5\times {10}^{5}V$
• B. $9\times {10}^{5}V$
• C. $9\times {10}^{4}V$
• D. Zero

Answer 1

The correct option is A $4.5\times {10}^{5}V$

Assume the point at which field is zero is at a distance X from $4\mu C$
$X=\frac{d}{\sqrt{\frac{q_2}{q_1}}+1}=\frac{50}{\sqrt{\frac{9}{4}}+1}=\frac{50}{\frac{3}{2}+1}=\frac{100}{5}=20cmV=V_1+V_2=\frac{1}{4\pi {ϵ}_0}[\frac{q_1}{r_1}+\frac{q_2}{r_2}]=9\times {10}^9[\frac{4\times {10}^{-6}}{0.2}+\frac{9\times {10}^{-6}}{0.3}]=9\times {10}^3[20+30]=9\times {10}^3\times 50=4.5\times {10}^{5}V$