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

The magnitude of the electric field produced by a charged sphere inside the sphere at a radial distance r from the sphere’s center can be calculated using Gauss's law.

Step-by-step explanation:

The magnitude of the electric field produced by the charged sphere inside the sphere at a radial distance r from the sphere’s center can be calculated using Gauss's law.

For 0 < r < R, the electric field is given by:

E = (ρr)/(3ε₀)

Where ρ is the volume charge density and ε₀ is the permittivity of free space.

Answer 2

The magnitude of Electric Field is
`E=(Qr)/(4\pi \epsilon_0 R^3)`

Step-by-step 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)=(Qr^3)/(R^3)`

Now using Gauss Law we have

`E*4\pi r^2=(q_(in))/(\epsilon_0)\\E*4\pi r^2=((Qr^3)/(R^3))/(\epsilon_0)\\E=(Qr)/(4\pi \epsilon_0 R^3)`