Question

Why gradient must exist to make constant electric field?

Answer 1

Electric field is a Force and potential or voltage is the energy required to overcome this force or the energy required to move a particle from one position to other .

When electrical field is zero, the energy required to overcome it will also be zero.

When a particle is to be moved from a point, say A to a point, say B such that the electric field intensity at A is equal to that at B, the net change in electric field experienced by the particle is zero, but the energy required to move the particle from A to B is not zero, so V is not equal to zero.

So, according to the equation

E = gradient(V),

When E is zero, V may or may not be zero