# Planck current

1 - conductors, FP - Planck force, lP - Planck length, IP - Planck current.

The Planck current is the unit of electric current, denoted by IP, in the system of natural units known as Planck units.

$I_\text{P} = q_\text{P}/t_\text{P} = (c^6 4 \pi \varepsilon_0 / G )^ \frac{1}{2}$ ≈ 3.479 × 1025 A

where:

$q_\text{P} = (c \hbar 4 \pi \varepsilon_0 )^ \frac{1}{2}$ is the Planck charge
$t_\text{P} = (\hbar G/c^5)^ \frac{1}{2}$ is the Planck time
$\varepsilon_0$ = permittivity in vacuum
$\hbar$ is the reduced Planck constant
G is the gravitational constant
c is the speed of light in vacuum.

The Planck current is that current which, in a conductor, carries a Planck charge in Planck time.

Alternatively, the Planck current is that constant current which, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section, and placed a Planck length apart in vacuum, would produce between these conductors a force equal to a Planck force per Planck length.