Planck current

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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.

Notes and references[edit]