(D) Let the magnetic moment of the weaker magnet be $M_1 = M$ and the stronger magnet be $M_2 = \sqrt{3} M$. Since they are joined in a cross (+) shap

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(D) Let the magnetic moment of the weaker magnet be $M_1 = M$ and the stronger magnet be $M_2 = \sqrt{3} M$. Since they are joined in a cross (+) shape,the angle between them is $90^{\circ}$. Let the weaker magnet make an angle $\theta$ with the earth's magnetic field $B_H$. Then the stronger magnet makes an angle $(90^{\circ} - \theta)$ with $B_H$. In equilibrium,the net torque acting on the system due to the earth's magnetic field must be zero. $\tau_1 + \tau_2 = 0$ $M_1 B_H \sin(\theta) = M_2 B_H \sin(90^{\circ} - \theta)$ $M \sin(\theta) = \sqrt{3} M \cos(\theta)$ $\tan(\theta) = \sqrt{3}$ $\theta = 60^{\circ}$.

Class 12 Physics Magnetism and Matter Magnetic field due to magnetic dipole and Dipole in Magnetic Field and Poential Energy and Work Done

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Two short bar magnets of magnetic moments $M$ and $\sqrt{3} M$ are joined like a cross (+). This cross is suspended from its centre with its plane horizontal in the earth's magnetic field. When the cross comes to equilibrium,the angle made by the weaker magnet with the earth's magnetic field $B_H$ is (in $^{\circ}$)

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Magnetism and Matter

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Magnetic field due to magnetic dipole and Dipole in Magnetic Field and Poential Energy and Work Done

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