Question

The electric field intensity at a point $P$ due to point charge $q$ kept at point $Q$ is $24 \,N \,C^{-1}$ and the electric potential at point $P$ due to same charge is $12\, J \,C^{-1}$. The order of magnitude of charge $q$ is

• A. $10^{-6} \, C$
• B. $10^{-7} \, C$
• C. $10^{-10} \, C$
• D. $10^{-9} \, C$

Answer 1

Answer: (D)

Electric field of a point charge,
$ E=\frac{1}{4\pi\varepsilon_{0}} \frac{q}{r^{2}}=24\, N \, C^{-1}$
Electric potential of a point charge,
$V=\frac{1}{4\pi\varepsilon_{0}}\frac{q}{r}=12 \, J \,C^{-1}$
The distance $PQ$ is
$r=\frac{V}{E}=\frac{12}{24}=0.5\, m $
$\therefore $ Magnitude of charge
$q'=4\pi\varepsilon_{0} \, Vr $
$=\frac{1}{9\times10^{9}}\times12 \times0.5$
$=0.667 \times 10^{-9} \, C$
$\approx 10^{-9} \, C$