Name: Hysteresis: Property of Ferromagnetic Substances
Uploaded: 2019-07-19
Duration: 5 min 6 s
Description: The behaviour of ferromagnets is fascinating. The magnetic field due to a ferromagnet exhibits an interesting phenomenon known as hysteresis. Let’s explore.

Question

Derive an expression for the magnetic field due to a magnetic dipole in broad side on position at a distance

r

from its centre. The length of the dipole is

2 l

and its magnetic moment is

m

.

Accepted Answer

Let a bar magnet of length $2 l$ and pole strength $m$ . Now imagine a unit north pole at point $P$ as shown in the figure.

Then from coulomb’s law of magnetic forces, the force exerted by the $N$ -pole of bar magnet over this unit north pole,

$F_{N} = \frac{μ_{0}}{4 π} . \frac{m}{x^{2}}$ , along $\vec{N P}$

Similarly, the force exerted by $S$ -pole on a unit north pole is

$F_{S} = \frac{μ_{0}}{4 π} . \frac{m}{x^{2}}$ , along $\vec{P S}$

As the magnitude of $F_{N}$ and $F_{S}$ are equal, their vertical components get cancelled while horizontal component adds up along $P R$ .

Hence, $B_{e q u a} = F_{N} \cos θ + F_{S} \cos θ = 2 F_{N} \cos θ$

$[∴ \cos θ = \frac{l}{x}]$

$= 2 (\frac{μ_{0}}{4 π} . \frac{m}{x^{2}}) . \frac{l}{x}$ $[∴ M = m \times 2 l]$

$= \frac{μ_{0}}{4 π} . \frac{M}{x^{3}}$

$[∴ x = {(r^{2} + l^{2})}^{1 / 2}]$

$B_{e q u a} = \frac{μ_{0}}{4 π} . \frac{M}{{(r^{2} + l^{2})}^{3 / 2}}$

For a short magnet $l ≪ r$ .

$∴ B_{e q u a} = \frac{μ_{0}}{4 π} . \frac{M}{r^{3}}$

Derive an expression for the magnetic field due to a magnetic dipole in broad side on position at a distance $r$ from its centre. The length of the dipole is $2 l$ and its magnetic moment is $m$ .

Important Questions on Magnetism

Learn and Prepare for any exam you want !

Derive an expression for the magnetic field due to a magnetic dipole in broad side on position at a distance r from its centre. The length of the dipole is 2l and its magnetic moment is m.

Important Questions on Magnetism

Learn and Prepare for any exam you want !

Derive an expression for the magnetic field due to a magnetic dipole in broad side on position at a distance $r$ from its centre. The length of the dipole is $2 l$ and its magnetic moment is $m$ .