Planck current

1 - conductors, F_P - Planck force, l_P - Planck length, I_P - Planck current.

The Planck current is the unit of electric current, denoted by I_P, 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.