First slide

Magnetic properties of matter

Question

A cylindrical bar magnet ( radius = 1 cm , length = 10 cm ) has field intensity of 1000 A/m . The magnetic moment in the bar if permeability of its material is $6.3 \times 10^{- 4} H / m$ is ----------

Moderate

A

$15.50 A m^{2}$
B

$15.70 A m^{2}$
C

$18.70 A m^{2}$
D

$20.7 A m^{2}$

Solution

We know $μ = μ_{0} (1 + χ)$
$χ = \frac{μ}{μ_{0}} - 1 = \frac{6.3 \times 10^{- 4}}{4 π \times 10^{- 7}} - 1 ≃ 500$
Intensity of magnetization
$I = χ H = 500 \times 1000 = 5 \times 10^{5} A / m$
$\Rightarrow$ Magnetic moment $(M) = I V$
$\Rightarrow M = I π r^{2} L$
$\Rightarrow M = 5 \times 10^{5} \times 3.14 \times {(10^{- 2})}^{2} \times (10 \times 10^{- 2})$
$\Rightarrow M = 15.70 A m^{2}$

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