Introduction to Electrodynamics · Problem 2.50

Electrostatics — David J. Griffiths

Physics · yukawa-potential-charge-density

Problem

The electric potential of some configuration is given by the expression

V(\mathbf{r}) = A\frac{e^{-\lambda r}}{r},

where

A

and

\lambda

are constants. Find the electric field

\mathbf{E}(\mathbf{r})

, the charge density

\rho(\mathbf{r})

, and the total charge

Q

[Answer: \rho = \epsilon_0 A(4\pi\delta^3(\mathbf{r}) - \lambda^2 e^{-\lambda r}/r)]