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Force between two identical short bar magnets whose centres are $r$ metre apart is $4.8\,N$ when their axes are in the same line. If the separation is increased to $2r$ metre, the force between then is reduced to?

Last updated date: 21st Jul 2024
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Hint:Let us first understand about the magnetic dipole. A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles when the source's size is reduced to zero while the magnetic moment remains constant.

Complete step by step answer:
It's a magnetic equivalent of the electric dipole, but it's not a perfect match. A true magnetic monopole, which is the magnetic equivalent of an electric charge, has never been found in nature. When you get farther away from a magnetic source, the magnetic field around it begins to resemble that of a magnetic dipole.

The difference between two magnetic dipoles, the angle between their centrelines and the Z-axis, and the angle between their centrelines and the X-axis are all expressed by the letters $I,\theta $ and $\varphi $. Force between two magnetic dipoles is:
$F = \dfrac{{{\mu _o} \times 6{M_1}{M_2}}}{{4\pi \times {r^4}}}$
Where, ${M_1}$ and ${M_2}$ are magnetic moments.
$\dfrac{{{F_2}}}{{{F_1}}} = {(\dfrac{{{r_1}}}{{{r_2}}})^4} \\
\Rightarrow \dfrac{{{F_2}}}{{{F_1}}} = {(\dfrac{1}{2})^4} \\
\Rightarrow \dfrac{{{F_2}}}{{{F_1}}} = \dfrac{1}{16}$
$\Rightarrow {F_2} = \dfrac{{{F_1}}}{{16}} \\
\Rightarrow {F_2} = \dfrac{{4.8}}{{16}} \\
\therefore {F_2} = 0.3\,N$

Hence, the force between then is reduced to 0.3 N.

Note:The interaction of one dipole with the magnetic field formed by the other dipole can be interpreted as the repulsion or attraction between two magnetic dipoles. When the magnetic dipole \[m\] is associated with $B$, for example, the energy is $ - mB$ and the force is in the direction of increasing \[B\].