Question

An insulating sphere with radius of 20cm carries a uniform volume charge density of 1.5×10-⁶ C/m³. Find the magnitude of the electric field at a point inside the sphere that lies 8.0 cm from the center

Answer 1

The Gauss' law says

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

$$\oint EdA=E*4\pi r^2$$

$$q_{enc}=\rho V=\rho*\frac{4}{3}\pi r^3$$

Thus

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

$$E=\frac{\rho r}{3\epsilon_0}=\frac{1.5*10^{-6}*0.08}{3*8.85*10^{-12}}=4.5*10^3\:\rm N/C$$