Answer to Question #104211 in Electricity and Magnetism for Akshay

Question

The electric potential at a point is given by
V = z(z² - 4x²). Calculate the electric field
E at that point

Answer 1

$\overrightarrow{E}=-\overrightarrow{\nabla}\cdot U$

$\frac{\partial U}{\partial x}=-8zx$

$\frac{\partial U}{\partial y}=0$

$\frac{\partial U}{\partial z}=3z^2-4x^2$

$\overrightarrow{E}=(8zx)\cdot\overrightarrow{i}-(3z^2-4x^2)\cdot \overrightarrow{k}$ Answer