# GRE Physics GR 1777 Problem Solution

## 005. Electrodynamics (Maxwell\’s Equations)

### Solution

In Maxwell\’s equations, Ampère\’s law (with Maxwell\’s correction) is
$latex \\nabla \\times \\vec{B} = \\mu_0 \\vec{J} + \\mu_0 \\epsilon_0 \\frac{\\partial \\vec{E}}{\\partial t}$.

We can write this equation as
$latex \\nabla \\times \\vec{B} – \\mu_0 \\epsilon_0 \\frac{\\partial \\vec{E}}{\\partial t} = \\mu_0 \\vec{J}$,
where $latex \\vec{J}$ is the current (the electric displacement current).

$latex \\frac{\\partial \\vec{E}}{\\partial t}$ is change of electric fields with respect to the time (rate of change of the electric flux).

If we assume that $latex \\nabla \\times \\vec{B} = 0$, and the current flows through a surface S, then we can clearly see that the electric displacement current through S is proportional to the rate of change of the electric flux through S.

### Alternative Solution

The definition of electric displacement current is
$latex \\vec{J}_{D} = \\epsilon_0 \\frac{\\partial \\vec{E}}{\\partial t} + \\frac{\\partial \\vec{P}}{\\partial t}$.