A magnetic dipole is acted upon by two magnet | vedclass

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(B) Let the two magnetic fields be $B_1 = 15 \, mT$ and $B_2$. The angle between them is $\alpha = 75^{\circ}$.In stable equilibrium,the torque exerte

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(B) Let the two magnetic fields be $B_1 = 15 \, mT$ and $B_2$. The angle between them is $\alpha = 75^{\circ}$.In stable equilibrium,the torque exerted by the two fields on the magnetic dipole must be equal and opposite.The torque on a dipole in a magnetic field $B$ is given by $	au = MB \sin 	heta$,where $	heta$ is the angle between the dipole moment $M$ and the field $B$.Let the dipole make an angle $	heta_1 = 30^{\circ}$ with $B_1$. Then the angle with $B_2$ is $	heta_2 = \alpha - 	heta_1 = 75^{\circ} - 30^{\circ} = 45^{\circ}$.For equilibrium,$MB_1 \sin 	heta_1 = MB_2 \sin 	heta_2$.$B_1 \sin 30^{\circ} = B_2 \sin 45^{\circ}$.$15 	imes \frac{1}{2} = B_2 	imes \frac{1}{\sqrt{2}}$.$B_2 = \frac{15 	imes \sqrt{2}}{2} = \frac{15}{1.414} \approx 10.6 \, mT$.Rounding to the nearest integer,$B_2 \approx 11 \, mT$.

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