Question

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80\mu C/m^2$.

(a) Find the charge on the sphere.

(b) What is the total electric flux leaving the surface of the sphere?

Answer 1

(a)

$d=2.4m$

$r=1.2m$

Surface charge density, $\sigma =80.0\mu C/m^2=80\times {10}^{-6}C/m^2$

Total charge on surface of sphere,

$Q=$ Charge density × Surface area

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

$=80\times {10}^{-6}\times 4\times 3.14\times (1.2{)}^2$

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

Therefore, the charge on the sphere is $1.447\times {10}^{-3}C$.

(b)

${\varphi }_{total}=\frac{Q}{{\in }_0}$

${\in }_0=8.854\times {10}^{-12}{N}^{-1}{C}^2{m}^{-2}$

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

${\varphi }_{total}=\frac{1.447\times {10}^{-3}}{8.854\times {10}^{-12}}$

$=1.63\times {10}^{8}N{C}^{-1}{m}^2$

Therefore, the total electric flux leaving the surface of the sphere is $1.63\times {10}^{8}N{C}^{-1}{m}^2$