Answer to Question #186248 in Field Theory for Berhad

Question

An insulating sphere has radius R and uniform volume charge density ρ. Calculate the electric field at the point P which is inside (r < R) and outside (r > R) of the sphere by using Gauss’s law. Here r is the distance between the center of the sphere and the point P. (b) Discuss the possibility of choosing Gaussian surface other than the sphere. For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric field of a charged sphere? Explain your answer in detail. 

Answer 1

a) inside (r < R)

$$E=\frac{r\rho}{3\epsilon_0}$$

outside (r > R)

$$E=\frac{R^3\rho}{3r^2\epsilon_0}$$

b)  Gaussian surface must be chosen from the symmetry of the electric field.

It is a wrong way to  choose the cylindrical surface as a Gaussian surface to use Gauss’s law in order to calculate the electric field of a charged sphere.