The force of repulsion between two similar magnetic poles each of strength \[2Am\] at a distance \[2m\] from each other in vacuum is:
a. \[{10^{ - 5}}N\]
b. \[{10^{ - 7}}N\]
c. \[{10^{ - 3}}N\]
d. \[2 \times {10^{ - 7}}N\]

Hint: The magnetic Coulomb law for the magnetic pole is equivalent to the electric charge. Coulomb law. According to this law, the Coulomb force is inversely proportional to the squared distance. This distance is taken between the Magnetic poles. This force may be a repulsive force which occurs between like poles (N–N, S–S) or may be an attractive force which acts between poles (N–S).

Formula used:
We are using Coulomb’s law of magnetism. According to this law, Attraction or repulsive force between two poles are given as \[F = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{{m_1}{m_2}}}{{{r^2}}}\]. Where, \[{m_1}\] and \[{m_2}\] are pole strengths of magnetic poles. \[\mu \] is the permeability constant and \[r\] is the distance of separation between poles.

Complete step by step answer:
Given: \[{m_1} = {m_2} = 2Am\], \[r = 2m\]and \[\dfrac{{{\mu _0}}}{{4\pi }} = {10^{ - 7}}\]
According to Coulomb’s law of magnetism, a force of attraction and repulsion is given by
\[F = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{{m_1}{m_2}}}{{{r^2}}}\]
Substituting values, we get
\[
\Rightarrow F = {10^{ - 7}} \times \dfrac{{2 \times 2}}{{{2^2}}} \\
\Rightarrow F = {10^{ - 7}}N \\
 \]

Hence, the correct answer is option (B).

Additional information:
If two magnetic poles of strengths are kept at a distance r apart from each other. Then force of attraction or repulsion between the two poles is directly proportional to the product of their pole strengths.
The pole strength depends on the nature of the magnet's material. It also depends upon the state of magnetization and area of cross-section. The North Pole experiences a force which has the direction of the magnetic field and the South Pole experiences a force opposite to the field. The unit of strength of a magnetic pole is ampere meter or newton/Tesla.

Note: Here, Formula for the Coulomb law is used. This formula is similar as gravitational force acts between two masses. Students can be confused in these two forces. Here\[{m_1}\] and \[{m_2}\] are pole strengths not masses. Students must have clear knowledge about pole strength.