Question

Give the relation between electric field and electric potential.

Answer 1

Consider a positive charge q kept fixed at the origin. To move a unit positive charge by a small distance dx in the electric field E, the work done is given by dW = -E dx. The minus sign implies that work is done against the electric field. This work done is equal to an electric potential difference. Therefore,

dW = dV.

(or) dV = -Edx

Hence E = `"dV"/"dx"`

The electric field is the negative gradient of the electric potential.