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Question -

A uniform magnetic field of 3000G is established along the positive z-direction. A rectangular loopof sides 10 cm and 5 cm carries a current of 12 A. What is the torque on theloop in the different cases shown in Fig. 4.28? What is the force on each case?Which case corresponds to stable equilibrium?



Answer -

Magnetic field strength, B =3000 G = 3000 × 10−4 T = 0.3 T

Length of the rectangular loop, l =10 cm

Width of the rectangularloop, b = 5 cm

Area of the loop,

A = l × b =10 × 5 = 50 cm= 50 × 10−4 m2

Current in the loop, I =12 A

Now, taking the anti-clockwisedirection of the current as positive and vise-versa:

(a) Torque, 

Fromthe given figure, it can be observed that is normal tothe y-z plane and B is directed alongthe z-axis.

The torque is  N m along thenegative y-direction. The force on the loop is zero because theangle between A and B is zero.

(b) Thiscase is similar to case (a). Hence, the answer is the same as (a).

(c) Torque 

From the given figure, it can beobserved that is normal to the x-z planeand B is directed along the z-axis.

The torque is  N m along thenegative direction and the force is zero.

(d) Magnitude of torqueis given as:

Torque is  N m at an angle of 240°with positive direction. The force is zero.

(e) Torque 

Hence, the torque is zero. Theforce is also zero.

(f) Torque 

Hence, the torque is zero. Theforce is also zero.

Incase (e), the direction of and is the same and the angle betweenthem is zero. If displaced, they come back to an equilibrium. Hence, itsequilibrium is stable.
Whereas,in case (f), the direction of and is opposite. The angle between them is 180°. Ifdisturbed, it does not come back to its original position. Hence, itsequilibrium is unstable.

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