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Question

A solid insulating sphere of radius R and total charge Q has a spherically symmetric
but non-uniform charge density given by p= Ar where A is a constant and r is
measured from the center of the sphere. Calculate the electric field at any radius r within the
sphere (i.e. for r<R)
Q/(4π ερ 12)
(Ar²)/(980)
(Ar³)/(5 &0)
(Ar5)/(5 R²80)
Q/(4π 0 R²)

Expert Solution

Step 1

Given: The radius of the insulating sphere is R.

The total charge is Q .

The charge density is ${Ar}^{6}$ .

To determine: The electric field at $r < R$

Assume a gaussian surface at radius r.

The charge enclosed in gaussian surface is

$q = \int_{0}^{r} ρdV$

The volume element is $dV = 4 {πr}^{2} dr$

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