In physics, the Planck charge, denoted by
q
P
, is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.
The Planck charge is defined as:
q
P
=
4
π
ϵ
0
ℏ
c
=
e
α
≈
1.875
5459
×
10
−
18
coulombs,
where
c
is the speed of light in the vacuum,
ℏ
is the reduced Planck constant,
ϵ
0
is the permittivity of free space
e
is the elementary charge
α
is the fine structure constant.
The Planck charge is
α
−
1
/
2
≈
11.706
times larger than the elementary charge e carried by an electron.
The Gaussian cgs units are defined so that
4
π
ϵ
0
=
1
, in which case
q
P
has the following simple form,
q
P
=
ℏ
c
.
It is customary in theoretical physics to adopt the Lorentz–Heaviside units (also known as rationalized cgs). When made natural (ħ=1, c=1), they are like the SI system with
ϵ
0
=
μ
0
=
1
. Therefore, it is more appropriate to instead define the Planck charge as
q
P
′
=
ϵ
0
ℏ
c
=
e
4
π
α
≈
5.291
×
10
−
19
coulombs.
When charges are measured in units of
q
P
′
, i.e., when
q
P
′
is set equal to 1, we obtain
α
=
e
2
4
π
,
which is commonly used in quantum field theory, so that e≅0.30282212088.
By contrast, in (non-rationalized) natural cgs units where
q
P
=
1
we have
α
=
e
2
.
