Question

A solid sphere 10 cm in radius carries a uniform 40-?C charge distribution throughout its volume. It is surrounded by a concentric shell 20 cm in radius, also uniformly charged with 40 ?C.

a)Find the electric field 5.0 cm from the center.

b)Find the electric field 15 cm from the center.

c)Find the electric field 30 cm from the center.

Answer 1

If charge is distributed uniformly in a sphere, then for finding electric field at or outside the surface, it can be assumed that the whole charge is concentrated at the centre of the sphere.
For finding electric field at a point inside the sphere, we should assume a second sphere, which is concentring with the first and goes through that point. We should ignore the charge outside the second sphere because electric field because of that charge is 0. We should consider only the charge within the second sphere.
According to Coulomb's law, the electric field at a distance r meter from a point charge q coulomb is
9 * 10^9 * q/r^2 N/C

a) 0 cm from the center means at the center. The charge is uniformly distributed. Therefore, the electric field at the center = 0.

b) Volume within sphere of radius 10.0 cm = 4/3 * pi * (10 cm)^3
Volume of the complete sphere = 4/3 * pi * (40 cm)^3
Charge per unit volume = 42/[4/3 * pi * (40 cm)^3]