Question

A uniformly charged conducting sphere of $2.4m$ diameter has a surface charge density of $80.0\mu C{m}^{-2}$.
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, $r=\frac{2.4}{2}=1.2m$
Surface charge density, $\sigma =80\mu C/m^2$
$=80\times 10^{-6}C{m}^{-2}$
Surface charge density $=\frac{\text{ Charge }}{\text{ Surface area }}$
$\sigma =\frac{q}{4\pi r^2}$
$q=\sigma \times 4\pi r^2=80\times 10^{-6}\times 4\times 3.14\times 1.2\times 1.2$
$q=1.4\times 10^{-3}C$