Physics - Electrostatics Question with Solution | TestHub

Key Idea Electric field at a point is equal to the negative gradient of the electrostatic potential at that point. Potential gradient relates with electric field according to the following relation $E=\frac{-dV}{dr}$ $$\begin{array}{rl}\vec{E}& =-\frac{\partial V}{\partial r}=\left[-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}-\frac{\partial V}{\partial x}\hat{k}\right]\\ & =\left[\hat{i}\left(2xy+z^3\right)+\hat{j}{x}^2+\hat{k}3x{z}^2\right]\end{array}$$