Q25 of 91 Page 230

Figure shows a circular wire-loop of radius a, carrying a current i, placed in a perpendicular magnetic field B.

(a) Consider a small part dl of the wire. Find the force on this part of the wire exerted by the magnetic field.


(b) Find the force of compression in the wire.




Given-



Radius of the circular wire = a



Electric current passing through the loop = i



Magnetic field Perpendicular to the plane = B




(a) Magnetic force due to presence of current on a small differential length dl given by –




where,


B= magnetic field


I = current


dl =differential length of the wire


and θ = the angle between B and dl



The direction of magnetic force,using Fleming’s left-hand rule is towards the centre for any differential length dl of the wire.


Also, dl and B are perpendicular to each other


(b) Suppose a part of loop subtends a small angle 2θ at the centre of a circular loop as shown in fig.



Then, looking into the fig. we can say



We know length l of an arc –



where ,


r is radius of the circle and the angle subtended by the arc at the center


here, the arc is subtending an angle 2θ





Since is small, sinθ will become negligible







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