Planck current

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1 - conductors, F_p - Planck force, l_p - Planck length, I_p - Planck current.

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

$I_p = q_p/t_p = (c^6 4 \pi \varepsilon_0 / G )^ \frac{1}{2}$ ≈ 3.479 × 10²⁵ A

where:

$q_p = (c \hbar 4 \pi \varepsilon_0 )^ \frac{1}{2}$ is the Planck charge

$t_p = (\hbar G/c^5)^ \frac{1}{2}$ is the Planck time

$\varepsilon_0$ = permittivity in vacuum

$\hbar$ is Dirac's 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.

Alternately, 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.

Planck's natural units

Base Planck units: Planck time | Planck length | Planck mass | Planck charge | Planck temperature