A magnetic dipole is under the influence of t | vedclass

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(B) In stable equilibrium,the net torque acting on the magnetic dipole is zero. The torque due to field $B_1$ must balance the torque due to field $B_

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$30$

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(B) In stable equilibrium,the net torque acting on the magnetic dipole is zero. The torque due to field $B_1$ must balance the torque due to field $B_2$.Let $M$ be the magnetic moment of the dipole. The torque due to $B_1$ is $	au_1 = M B_1 \sin(90^{\circ} - 	heta) = M B_1 \cos 	heta$.The torque due to $B_2$ is $	au_2 = M B_2 \sin 	heta$.For equilibrium,$	au_1 = 	au_2$,so $M B_1 \cos 	heta = M B_2 \sin 	heta$.Rearranging the terms,we get $	an 	heta = \frac{B_1}{B_2}$.Substituting the given values:$	an 	heta = \frac{0.5 	imes 10^{-3}}{0.866 	imes 10^{-3}} = \frac{0.5}{0.866} \approx \frac{0.5}{0.5 \sqrt{3}} = \frac{1}{\sqrt{3}}$.Since $	an 	heta = \frac{1}{\sqrt{3}}$,we have $	heta = 30^{\circ}$.

$A$ magnetic dipole is under the influence of two orthogonal magnetic fields,$B_1 = 0.5 \times 10^{-3} \ T$ and $B_2 = 0.866 \times 10^{-3} \ T$. If the dipole comes to stable equilibrium at an angle $\theta$ with respect to the $B_2$ field,then the value of $\theta$ is (in $^{\circ}$)

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