9. A rectangular coil of size 3.0 c...

9. A rectangular coil of size 3.0 cm x 40 cm and having 100 turns, is pivoted about the z-axis as shown in figure (34-W7). The coil carries an electric current of 2:0 A and a magnetic field of 1.0 T is present along the y-axis. Find the torque acting on the coil if the side in the x-y plane makes an angle 0 = 37° with the x-axis. N A 2A Figure 34-67

JEE/Engineering Exams
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(b) 'The magnetic moment of the loop is ( vec{mu}=n i vec{A} ) where ( n ) is the number of turns, ( i ) is the current and ( overrightarrow{mathrm{A}} ) is the area-vector. The direction of ( overrightarrow{mathrm{A}} ) is determined by the sense of the current and in this case it lies in the fourth quadrant making an angle ( theta=37^{circ} ) with the negative ( Y ) -axis. Torque [ begin{aligned} vec{Gamma}=vec{mu} times vec{B} &=n vec{A} times vec{B} . text { Thus, } Gamma &=100 times(2 mathrm{A}) timesleft(12 times 10^{-4} mathrm{m}^{2}right) times 1 mathrm{T} times sin 37^{circ} &=0.14 mathrm{N}-mathrm{m} end{aligned} ] The torque is along the positive Z-axis.
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