NS is the bar magnet of length 2l and of pole strength m. P is a point on the axial line at a distance d from its mid point O (Fig.).
According to inverse square law,

**Magnetic induction at a point along the axial line due to a
magnetic dipole (Bar magnet)**

NS
is the bar magnet of length 2l and of pole strength m. P is a point on the axial
line at a distance d from its mid point O (Fig.).

According
to inverse square law,

F
= ?_{0}/ 4 π . m_{1}m_{2}/d^{2}

∴ Magnetic induction (B_{1})
at P due to north pole of the magnet

B_{1}
= ?_{0}/4 π . m/NP^{2}
along NP

=
?_{0}/4 π . m/(d-*l*)^{2} along NP

Magnetic
induction (B_{2}) at P due to south pole of the magnet,

B_{2}
= ?_{0}/4 π . m/(SP)^{2}
along PS

B_{2}=
?_{0}/4 π . m/(d+*l*)^{2} along PS

Magnetic
induction at P due to the bar magnet,

B
= B_{1} ? B_{2}

B
= ?_{0}/4 π . 2Md/(d^{2}-*l*^{2})^{2}

where
M = 2ml (magnetic dipole moment).

For
a short bar magnet, *l* is very small
compared to d, hence l ^{2} is
neglected.

∴ B = ?_{0}/4 π
. 2Md^{3}

The
direction of B is along the axial line away from the north pole.

*Coulomb?s inverse square law*

Coulomb?s inverse square law
states that the *force of attraction or*
*repulsion between the two magnetic poles
is directly proportional to the product of their pole strengths and inversely
proportional to the square of the distance between them.*

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