First slide

Magnetism

Question

In an uniform field the magnetic needle completes 10 oscillations in 92 seconds. When a small magnet is placed in the magnetic meridian 10cm due north of needle with north pole towards south completes 15 oscillations in 69 seconds. The magnetic moment of magnet is ………… $A - m^{2}$ (given $B_{H} = 0.3 G$ )

Moderate

Solution

$n = \frac{1}{2 π} \sqrt{\frac{M B}{I}} \frac{10}{92} α \sqrt{B_{H}} ............. (1) \frac{15}{69} α \sqrt{B - B_{H}} ............. (2) F r o m (1) & (2) \Rightarrow B = 5 B_{H} W e k n o w t h a t, B = \frac{μ_{o}}{4 π} \frac{2 M}{d^{3}} \Rightarrow 5 B_{H} = 10^{- 7} \frac{2 M}{{(10 x 10^{- 2})}^{3}} \Rightarrow 5 x 0.3 x 10^{- 4} = 10^{- 7} x 10^{3} x 2 M \Rightarrow M = 0.75 A m^{2}$

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