First slide

Magnetism

Question

A bar magnet of magnetic moment ‘M’ is bent in the form of an arc which makes angle $60^{0}$ . The percentage change in magnetic moment is

Moderate

A

9% increase
B

9% decrease
C

4.5% decrease
D

4.5% increase

Solution

If the bar magnet is bent in the form of an arc making an angle $θ$ at the centre then its new magnetic moment is
$M^{1} = \frac{2 M \sin \frac{θ}{2}}{θ (r a d)} θ = 60 ° = \frac{π^{C}}{3} M^{1} = \frac{2 M \sin 30}{π} \times 3 M^{1} = \frac{2 M \times 3}{2 (π)} \times 3 = \frac{3 M}{π}$
Percentage change in magnetic moment is
$\frac{Δ M}{M} \times 100 = \frac{M^{1} - M}{M} \times 100 \begin{array}{l} = (\frac{\frac{3 M}{π} - M}{M}) \times 100 \\ = \frac{3 M - π M}{M π} \times 100 \end{array} \begin{array}{l} = \frac{M (3 - π)}{M π} \times 100 \\ = (\frac{3 - 3.14}{3.14}) \times 100 \end{array}$

$= - 4.5 % = D e c r e a s e s b y 4.5 %$

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