First slide

Magnetism

Question

A magnet is 10 cm long and its pole strength is 120 CGS units(1 CGS unit of pole strength=0.1 Am). Find the magnitude of magnetic field ‘B’ at a point on its axis at a distance 20 cm from it.

Moderate

A

${1.7×10}^{-5} T$
B

${3.4×10}^{-5} T$
C

${3.4×10}^{-6} T$
D

${1.7×10}^{-6} T$

Solution

The pole strength is m=120 CGS units= 12 Am
Magnetic length (distance between poles) is $2 l = 10 c m$ or $l = 0.05 m$
Distance from the center of magnet is d=20 cm=0.2 m.
The field B at a point on axial position is
$B = \frac{μ_{0}}{4 π} . \frac{2 M d}{{(d^{2} - l^{2})}^{2}}$
$\Rightarrow B = \frac{μ_{0}}{4 π} . \frac{4 m l d}{{(d^{2} - l^{2})}^{2}}$
$\Rightarrow B = [10^{- 7}] . \frac{4 \times 12 \times 0.05 \times 0.2}{{[{(0.2)}^{2} - {(0.05)}^{2}]}^{2}}$
$B = 3.4 \times 10^{- 5} T$ .

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