First slide

Magnetism

Question

The dipole moment of a coil of area ‘A’ and no. of turns N and carrying current (i) will be

Easy

A

$N i A$
B

$N^{2} i A$
C

$N i A^{2}$
D

$N i^{2} A$

Solution

We know magnetic field induction at a point ‘P’ at a distance r from the center of the circular coil is
$B = \frac{μ_{0} n i r^{2}}{2 {(r^{2} + x^{2})}^{\frac{3}{2}}}$ If $r > > x$
$B = \frac{μ_{0} n i r^{2}}{2 {(r)}^{3}} \times \frac{2 π}{2 π}$
$\Rightarrow B = \frac{2 (μ_{0} n i r^{2})}{4 π r^{3}} = \frac{μ {}_{0}}{4 π} \frac{2 n i A}{r^{3}}$ -------------(1)
We know magnetic field induction at a point ‘p’ on the axial line due to short bar magnet is
$B = \frac{μ {}_{0}}{4 π} \frac{2 M}{r^{3}}$ --------------(2)
Comparing (1) & (2) we get $M = n i A$

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