Q. 184.0( 12 Votes )

(a) Derive the ex

Answer :

Consider a loop ABCD in a uniform magnetic field with strength . Let the magnetic field make an angle with the normal of the loop. Let the current through the loop be .



The force acting on the arms BC and AD are equal and opposite. Also, they are collinear. Hence, they produce no torque.


Now, consider force and on arms AB And CD respectively.



Their direction is given by the right hand rule. These two forces are not collinear. The net torque is given by:




where A is the area of the coil.


The magnetic moment of the loop is given by:



where the direction of the area vector is given by the right hand thumb rule. We can see that the angle between and is .


Thus,



(b)


From the previous section,



Even though this result was derived for a rectangular loop, it is true in general for any current-carrying loop in a magnetic field. We can see that the torque () is maximum when . It is zero when . A radial magnetic field ensures that the angle is always irrespective of the rotation of the coil. Hence, the torque is always maximum even if the coil rotates.



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