A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/4 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

Given that,

Sphere of radius R

At radial distance ¼R it has an electric field of Eo

Magnitude of electric field E at r=2R

Solution

electric field is given as

E=KQ/r²

Now at R,

E=KQ/R²

When, at r=R/4 inside the sphere is given as

Eo=kQ/R³ • R/4

Eo=kQ/4R²

When, r = 2R

Then,

E=kQ / (2R) ²

E=kQ/4R²

Comparing this to Eo

Then, E=Eo

Then, the electric field at r=2R is equal to the electric field at r=R/4