Question

A solid conducting sphere with an area of 16 m 2 has a total charge of 4 μC. Determine the electric field through the Gaussian surface.

Answer 1

Given:

$A=\rm 16\:\rm m^2$

$q=\rm 4\:\mu C=4*10^{-6}\: C$

$\epsilon_0=8.85*10^{-12}\: \rm F/m$

The Gauss's law says

$$\phi=\oint EdA=\frac{q}{\epsilon_0}$$

For constant field

$$EA=\frac{q}{\epsilon_0}$$

$$E=\frac{q}{\epsilon_0 A}=\frac{4*10^{-6}}{8.85*10^{-12}*16}=2.8*10^4\:\rm V/m$$