Question

Show that electric field at any point is equal to the negative of the potential gradient at that point.

Answer 1

Explanation:

so we can prove mathematically that electric field is negative gradient of potential

Answer 2

E= −∇V

We know that force and potential energy are related to each other and is given by an equation

U = - ( Integra of F.dr)

here U is the potential energy, F is the Coulombian force acting on a charge, r is the displacement of unit charge

we can write it as

F = -dU/dr or F = −∇U

this is called the gradient of U

we also know that F = qE

here q is the charge and E is electric field present

so we can write it as

qE = −∇U

Also, V = U/q

here V is potential energy

So, E = −∇V

Therefore, we can say that the electric field at any point is equal to the negative of the potential gradient at that point.