Electric Field due to a Uniform Sphere of Charge
Consider a uniform spherical charge distribution in which a charge Q is uniformly distributed over the volume of a sphere of radius R.
The volumetric charge density is given by,
(as the distribution of charge is uniform)
Case 1: Field outside the sphere (radial distance > R).
The field has spherical symmetry
By Gauss's law,
[Note that the result is same as that of a point charge]
Case 2: Field inside the sphere (radial distance < R).
Consider a Gaussian sphere inside the sphere of charge.
Q = total charge of sphere
Q' = charge enclosed by the Gaussian sphere
Consider a uniform spherical charge distribution in which a charge Q is uniformly distributed over the volume of a sphere of radius R.
The volumetric charge density is given by, (as the distribution of charge is uniform)Case 1: Field outside the sphere (radial distance > R).
The field has spherical symmetry
By Gauss's law,
[Note that the result is same as that of a point charge]
Case 2: Field inside the sphere (radial distance < R).
Consider a Gaussian sphere inside the sphere of charge.
Q = total charge of sphere
Q' = charge enclosed by the Gaussian sphere
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