Question

Which charge configuration produces a uniform electric field?
A) point charge
B) infinite uniform line charge
C) uniformly charged infinite plane
D) uniformly charged spherical shell

Answer 1

A uniform electric field is that which does not change its magnitude or direction irrespective of the distance and position of the position of the point we are measuring the electric field at. We will use this information to determine which configuration produces a uniform electric field

Complete step by step answer
We’ve been asked to find a charge configuration that produces a uniform electric field. As mentioned in the hint, a uniform electric field is which remains constant in space regardless of the point where we are measuring it.
For a point charge, the electric field varies with the distance of the point of interest from the point charge as:
$\Rightarrow E \propto \dfrac{1}{{{r^2}}}$
So, a point charge does not create a uniform electric field.
For a uniform line charge, the electric field varies as a distance of the point of interest from the line as
$\Rightarrow E \propto \dfrac{1}{r}$
Again, the electric field decreases with increasing distance from the line so it does not create a uniform electric field.
For an infinite uniformly charged infinite plane, the electric field only depends on the surface charge density of the plane so it is independent of the distance and hence it remains constant in space. So, an infinite uniformly charged plane generates a uniform electric field.

Hence the correct choice is option (C).

Note
Since in reality, we don’t have an infinite charged plane, we can consider a plane to be infinitely large when the point at which we are measuring the electric field is very close to the plane when compared to the dimensions of the plane. The electric field on two sides of the uniformly charged infinite plane will have opposite directions however their magnitude will be constant.