Question

A uniformly charged conducting sphere of 2.4 m diameter has a
surface charge density of 80.0 $\mu C/m^2$.
Find the charge on the sphere.

What is the total electric flux leaving the surface of the
sphere?

Answer 1

Given, diameter of sphere =2.4m
Radius of sphere $r=\frac{2.4}{2}=1.2m$
Surface charge density =$\frac{Chrge}{Surfacearea}$
$\sigma =\frac{q}{4\pi r^2}q=\sigma \times 4\pi r^2=80\times {10}^{-6}\times 4\times 3.14\times 1.2\times 1.2q=1.4\times {10}^{-3}C$

$Totalflux=\varphi$
Using Gauss's theorem,
$Totalfluxleavingthesurface\varphi =\frac{Totalcharge}{{\epsilon }_0}{\epsilon }_0=\frac{q}{{\epsilon }_0}=\frac{1.45\times {10}^{-3}}{8.854\times {10}^{-12}}\varphi =1.6\times {10}^{8}N-m^2/C$
Thus, the flux leaving the surface of sphere is $1.6\times {10}^{8}N-m^2/C.$