Question

A uniformly charged sphere of diameter $2.4m$ has surface charge density of $80pC/m^2.$ Determine the total electric flux leaving out the spherical surface along with the spherical charge.

Answer 1

(a) Surface charge density on surface of uniformly charged sphere

$\sigma =\frac{q}{A}=\frac{q}{4\pi r^2}$

$q=4\pi r^2\sigma$

$=4\times 3.14\times 1.2\times 1.2\times 80.0\times {10}^{-6}C$

$=1447\times {10}^{-6}C$

$=1.447\times {10}^{-3}C$

$=1.45\times {10}^{-3}C=1.45mC$

(b) From Gauss's law if we consider surface as a gaussian surface then total charge on sphere will be bound to sphere.

$\therefore$ Leaving out flux through surface

${\varphi }_E=\frac{q}{{ϵ}_0}=\frac{1.45\times {10}^{-3}}{8.854\times {10}^{-12}}$

${\varphi }_E=1.6\times {10}^{8}N{m}^2{C}^{-1}$