Consider a positive charge q kept fixed at the origin. To move a unit positive charge by a small distance \(d x\) in the electric field \(E\), the work done is given by \(d W=-E d x\). The minus sign implies that work is done against the electric field. This work done is equal to electric potential difference. Therefore,
\(d W=d V\)
(Or) \(d v=-E d x\)
Hence \(\mathbf{E}=\frac{d V}{d x}\)
The electric field is the negative gradient of the electric potential.
