Question

A thin spherical shell of metal has a radius of 0.25m and carries charge of 0.2 microcoloumb . calculate the electric intensity just outside the shell.

Answer 1

Apply the Gauss's law we get

$$\phi=\oiint_{S}\overrightarrow{E}\cdot d\overrightarrow{A}=\frac{q_{enclosed}}{\epsilon_0}$$

Thus, in this case as spherical shell is symmetric, thus

$$E\oiint_{S}dA=\dfrac{2\times 10^{-7}}{\epsilon_0}\\ \implies E(4\pi r^2)=\dfrac{2\times 10^{-7}}{\epsilon_0}\\\implies E=\dfrac{1}{4\pi\epsilon_0}\dfrac{2\times 10^{-7}}{0.25^2}=9\times 10^9\times 2 \times 10^{-7}/0.25^2=28800N/C$$