Question

An insulating sphere with a radius of 20 cm caries a uniform volume charge density of 1.5×10^-6 C/m^3. Find the magnitude of the electric field of a point inside the sphere that lies 8.0cm from the center

Answer 1

The Gauss's law says

$$\oint EdA=\frac{q_{enc}}{\epsilon_0}$$

$$E*4\pi r^2=\frac{4\pi\rho r^3}{3\epsilon_0}$$

$$E=\frac{\rho r}{3\epsilon_0}=\frac{1.5*10^{-6}*0.08}{3*8.85*10^{-12}}=4520\:\rm N/C$$