The
force between two
charged particles is given by:
F = Q
1Q
2 / 4πε
0r
2
Where Q
1 and Q
2 are the charges on
point charges 1 and 2 respectively, ε
0 is the
permittivity of free space (8.85x10
-12 Fm
-1)
Sometimes the
equation is simplified to:
F = kQ
1Q
2 / r
2
Where k = 1 / 4πε
0 = 8.988x10
9This simplified version only works when the permittivity of the space the
interaction is taking place in is equal to that of free space.
Here is an example, an electron and an alpha particle (helium nucleus) are seperated by 1 centimetre, the force between them is:
F = 1.6x10
-19 x 3.2x10
-19 / 4πε
00.01
2
F = 5.12x10
-38 / 1.11212379x10
-10 x 0.01
2
F = 5.12x10
-38 / 1.11212379x10
-14
F = 5.12x10
-38 / 1.11212379x10
-14
F = 4.603x10
-24 N, which is very small.
Suppose the seperation wasn't 1
centimetre, but 1
millimetre:
F = 1.6x10
-19 x 3.2x10
-19 / 4πε
00.01
2
F = 5.12x10
-38 / 1.11212379x10
-10 x 0.001
2
F = 5.12x10
-38 / 1.11212379x10
-16
F = 5.12x10
-38 / 1.11212379x10
-16
F = 4.603x10
-22 N, which is 2
orders of magnitude higher for a 1 order of magnitude reduction in
seperation. This is due to the
inverse square law.