# Suppose that the radius of cross section of the wire used in the previous problem is r. Find the increase in the radius of the loop if the magnetic field is switched off. The Young modulus of the material of the wire is Y.

Given-

Radius of cross section of the wire used in the previous

problem = r

Young’s modulus of the metallic wire = Y.

It said in the question that, when the applied magnetic field is switched off, the tension in the wire increased and so iyd length is increased.

We know Young’s modulus,

we know, stress is, s is –

and strain

Young’s modulus,

Area of circle

Let, a be the radius of loop

from (1)

Now the tensile force will be the magnetic force acting on a conductor of length l given by –

where,

B= magnetic field

I = current

a =differential length of the wire

and θ = the angle between B and a

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