Question

Imagine that you have a sphere where a certain amount of charge is distributed. The electric charge density is not same within the sphere. The density within the outer half of the sphere is twice of that within the inner half of the sphere. Estimate how large the electric field is when measured at 3 meters away from the center. Assume that the total charge within the sphere is 84 Coulombs and the radius of the sphere is 4 meters and the permittivity constant is unity.

Answer 1

Electric Field at a point from the center of the charge is given by

where Q is the charge enclosed and is given by charge density times the volume enclosed. Where volume charge density is given by

Now charge q enclosed inside the smaller sphere of radius r = 3 m

Now electric field at the given distance

Now Plugging all the values