Question

A solid sphere of radius R is made of an insulating material. It holds a charge, Q, which is distributed evenly throughout the sphere and gives it a uniform volume charge density rho. What is the magnitude of the electric field produced by the charged sphere inside the sphere at a radial distance r from the sphere’s center, where 0 < r < R?

Answer 1

Answer:

The magnitude of Electric Field is $E=\dfrac{Qr}{4\pi \epsilon_0 R^3}$

Explanation:

Given:

• Radius of the solid sphere=R
• Total charge of the sphere=Q

Let consider a Gaussian surface at a distance of r such that  0<r>R in the shape of sphere such that the electric Field due to this E and it is radially outwards.

The charge inside this Gaussian surface volume we have , $q_{in}=\dfrac{Qr^3}{R^3}$

Now using Gauss Law we have

$E\times4\pi r^2=\dfrac{q_{in}}{\epsilon_0}\\E\times4\pi r^2=\dfrac{\dfrac{Qr^3}{R^3}}{\epsilon_0}\\E=\dfrac{Qr}{4\pi \epsilon_0 R^3}$