# Ampere's Law

on . Posted in Electromagnetism

Ampere's Law is a basic principle in electromagnetism that stated the magnetic field at a point along a closed loop is directly proportional to the total current passing through the loop and inversely proportional to the distance from the point to the wire.  Ampere's Law is particularly useful for calculating the magnetic field produced by simple symmetric current distributions, such as long straight wires, solenoids, and toroids.  It provides a quantitative way to determine the strength and direction of the magnetic field in various practical situations.

It's important to note that Ampere's Law applies to steady state, time invariant currents.  For cases involving time varying electric fields or changing currents, Ampere's Law may be modified or extended by including additional terms to account for the changing electromagnetic fields, as described by Maxwell's equations.

### Ampere's Law formula

$$\bigtriangledown x\; H = ( \partial D \;/\; \partial t ) + J$$
Symbol English Metric
$$\bigtriangledown x$$ = divergence operator $$ft \;/\; sec$$ $$m\;/\;s$$
$$H$$ = magnetic field strength $$T$$ $$kg\;/\;s^2-A$$
$$D$$ = electric displacement infinitesimal change $$ft\;/\;sec$$ $$m\;/\;s$$
$$t$$ = time infinitesimal change $$sec$$ $$s$$
$$J$$ = electric current density - $$A\;/\;m^2$$