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Question

Two circular coils C and D have equal number of turns and carry equal currents in the same direction in the same sense and subtend same solid angle at point O as shown in figure. The smaller coil C is midway between O and D. If we represent magnetic field induction due to bigger coil and smaller coil C as BD and BC respectively, then BD/BC is
679155_097b683d965b4bf5aa93deba480f549a.png

A
1:4
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B
1:2
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C
2:1
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D
1:1
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Solution

The correct option is B 1:2
Since two coils subtend the same solid angle at O, hence area of coil D=4x area of coil C
Therefore, radius of coil D=2× radius of coil C
BD=μ04π2π/(2r)2[(2r)2+a2]3/2
and BC=μ04π2πl(r)2[r2+(a/2)2]3/2
BDBC=4(4r2+a2)3/2×[4r2+a24]3/2
=48=12.
714023_679155_ans_aac3cf81d42040ffbac100e45a08a00b.png

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