A magnet is suspended in the magnetic meridian with un twisted wire. The upper end of the wire is rotated through $$1800$$ to deflect the magnet by $$300$$ from magnetic meridian. Now this magnet is replaced by another magnet. Now the upper end of the wire is rotated through $$2700$$ to deflect the magnet $$300$$ from the magnetic meridian. The ratio of the magnetic moments of the two magnets is

Question

A magnet is suspended in the magnetic meridian with un twisted wire. The upper end of the   wire is rotated through $$1800$$ to deflect the magnet by $$300$$ from magnetic meridian. Now this magnet is replaced by another magnet. Now the upper end of the wire is rotated through $$2700$$ to deflect the magnet $$300$$ from the magnetic meridian. The ratio of the magnetic moments of the two magnets is

Infinity Learn · Accepted Answer

During equilibrium, Torsional torque should be balanced by magnetic torque.     $$C($$α$$-$$θ$$)=MBsin$$θWhere  C is the couple per unit deflection & α is the twisted angle,  θ is the deflection angleGiven : α$$1=180$$°,θ$$=30$$°,  α$$2=270$$°   for first magnet  $$C(180-30)=M1Bsin30$$° for second magnet $$C(270-30)=M2Bsin30$$                     Dividing,        $$150240=M1M2=58$$

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