Question

A uniformly charged conducting sphere of $2.4\,m$ diameter has a surface charge density of $80.0\, \mu Cm ^{-2}$.
What is the charge on the sphere?

• A. $0.7 \times 10^{-1} C$
• B. $1.4 \times 10^{-2} C$
• C. $1.4 \times 10^{-3} C$
• D. $1.7 \times 10^{4} C$

Answer 1

Answer: (C)

Radius of shpere, $r=\frac{2.4}{2}=1.2 m$
Surface charge density, $\sigma=80 \mu C / m ^{2}$
$=80 \times 10^{-6} Cm ^{-2}$
Surface charge density $=\frac{\text { Charge }}{\text { Surface area }}$
$\sigma=\frac{q}{4 \pi r^{2}}$
$ q =\sigma \times 4 \pi r^{2}=80 \times 10^{-6} \times 4 \times 3.14 \times 1.2 \times 1.2 $
$ q =1.4 \times 10^{-3} C $