Question

c) Derive the expression for potential difference between two points in electric
field. (3)

Answer 1

Answer:

Consider two points A and B separated by a small distance dx in an electric field.

Since dx is small, the electric field E is assumed to be uniform along AB. The force acting on a unit positive charge at A is equal to E.

Now, the work done in moving a unit positive charge from A to B against the electric field is dW=−E×dx.

The negative sign shows that the work is done against the direction of the field. Since the work done is equal to potential difference dV between A and B then dV=−E×dx or E=−

dx

dV

Thus, the electric field at a point is the negative of the potential gradient at that point.