Question

A unit magnetic dipole is that pole which repels an identical pole at a \[1\] meter distance with a force of _____.
A. \[{10^{ - 6}}\,{\text{N}}\]
B. \[{10^{ - 7}}\,{\text{N}}\]
C. \[{10^{ - 5}}\,{\text{N}}\]
D. \[{10^{ - 4}}\,{\text{N}}\]

Answer 1

Hint: First we will find the expression for force exerted by two poles on each other which are separated by a certain distance precisely Coulomb’s law of magnetism. We will substitute the values and manipulate accordingly.

Complete step by step answer:
In the given question, we are supplied with the following data:
The magnetic dipole is of magnitude \[1\] .
It means that the pole strength of each pole is \[1\,{\text{Am}}\] .
The distance of separation between the two poles is \[1\] meter.
We are asked to find the force of repulsion between these two poles which are identical in nature. They are identical in the sense that both are of the same polarity.
So, we have,
\[{m_1} = 1\,{\text{Am}}\]
\[{m_2} = 1\,{\text{Am}}\]
\[r = 1\,{\text{m}}\]
\[{\mu _0} = 4\pi \times 1{0^{ - 7}}\,{\text{Tm}}{{\text{A}}^{ - 1}}\]

To calculate the force of repulsion between these two poles, we apply the formula which is the Coulomb’s law of magnetism:
\[F = \dfrac{{{\mu _0}}}{{4\pi }} \times \dfrac{{{m_1}{m_2}}}{{{r^2}}}\] …… (1)
Where,
\[{\mu _0}\] indicates permeability constant.
\[{m_1}\] and \[{m_2}\] indicates pole strength.
\[r\] indicates distance of separation.
Substituting the required values in the equation (1), we get:
\[\begin{gathered}
  F = \dfrac{{4\pi \times 1{0^{ - 7}}}}{{4\pi }} \times \dfrac{{1 \times 1}}{{{1^2}}} \\
  F = {10^{ - 7}}\,{\text{N}} \\
\end{gathered} \]
Hence, the required force is found out to be \[{10^{ - 7}}\,{\text{N}}\] .

So, the correct answer is “Option B”.

Additional Information:
A type of physical phenomenon that is driven by magnetic fields is magnetism. Electric currents and elementary particles' magnetic moments give rise to a magnetic field operating on other currents and magnetic moments. One part of the combined electromagnetism phenomena is magnetism.
As they draw or repel each other, magnetism is the energy exerted by magnets. The acceleration of electric charges induced magnetism. Any object consists of tiny atoms called units. There are electrons in every molecule, ions that bear electric charges. The electrons orbit the nucleus, or heart, of an atom, like spinning tops. Their motion induces an electrical current which allows any electron to behave like a microscopic magnet.

Note:
While solving this problem, remember that it is the case of identical poles. They both have unit magnitude, which means they are of magnitude \[1\] . Poles with different polarities will always attract each other. Had it been the case of non-identical poles and the distance same, then also the force would come out the same magnitude that we have just obtained, but it would be attracting in nature rather than repulsion.