Magnetism Question 239
Question: A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is $ 60{}^\circ $ and one of the fields has a magnitude of $ 1.2\times {{10}^{-2}}T $ . If the dipole comes to stable equilibrium at an angle of $ 15{}^\circ $ with this field, what is the magnitude of other field?
Options:
A) $ 4.4\times {{10}^{-3}},tesla $
B) $ 5.2\times {{10}^{-3}},tesla $
C) $ 3.4\times {{10}^{-3}},tesla $
D) $ 7.8\times {{10}^{-3}},tesla $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given that : $ B _{1}=1.2\times {{10}^{-2}},T $ , orientation of dipole with the field $ B _{1},{\theta _{1}}=15^{o} $ Hence, orientation of dipole with $ B _{2} $ , $ {\theta _{2}}=60^{o}-15^{o}=45^{o} $ (figure) As the dipole is in equilibrium, therefore, the torque on the dipole due to the two fields must be equal and opposite. If M be the magnetic dipole moment of the dipole, then $ {\tau _{1}}={\tau _{2}} $ or $ MB _{1},\sin ,{\theta _{1}}=MB _{2},\sin ,{\theta _{2}} $ or, $ B _{2}=\frac{B _{1},\sin ,{\theta _{1}}}{\sin ,{\theta _{2}}}=\frac{1.2\times {{10}^{-2}},\sin ,15^{o}}{\sin ,45^{o}} $
$ =\frac{1.2\times {{10}^{-2}}\times 0.2588}{0.7071}=4.4\times {{10}^{-3}},Tesla $
BETA
