Q. 253.7( 3 Votes )

# 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.

Answer :

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, d*l* and B are perpendicular to each other

(b) Suppose a part of loop subtends a small angle 2*θ* 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 2*θ*

Since is small, sinθ will become negligible

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