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Q.

A thin ring of radius 10 cm carrying a current of 10 A is placed in a uniform magnetic field of induction 1.5 T with its plane perpendicular to the field. Then tensile or compressive force induced in the wire of the ring is 

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a

1.8 N

b

2.1 N

c

1.5 N

d

1.2 N

answer is C.

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Detailed Solution

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Case (i): For clockwise current and magnetic field into the paper, force induced in the wire is tensile in nature.

 Force acting on each element of length L of the ring is radially outwards and F=i.L.B

F' = Force per unit length =FL=iB

For equilibrium, 2T=F' x 2r=iB x 2r

T=irB=10 x 0.1 x 1.5 N=1.5 N

Case (ii): For clockwise current and magnetic field out of the paper, force induced in the wire is same as in the above case except that now it is compressive in nature.

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