Two circular coils X and Y having equal number of turns and carry equal currents in the same sense and subtend same solid angle at point O. If the smaller coil X is midway between O and Y, then if we represent themagnetic induction due to bigger coil Y at O as BY and due to smaller coil X at O as BX, then
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a
BYBX=1
b
BYBX=2
c
BYBX=12
d
BYBX=14
answer is C.
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Detailed Solution
Magnetic induction at O due to coil Y is given byBY=μ04π×2πi(2r)2(2r)2+(d)23/2………………(1)Similarly, the magnetic induction at O due to coil X is given byBX=μ04π×2πi(r)2(r)2+(d/2)23/2…………….(2)From eqs. (1) ad (2),BYBX=12