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Question: Two circular coils X and Y having equal number of turns and carry equal currents in the same sense a...

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 the magnetic induction due to bigger coil Y at O as BY and due to smaller coil X at O as BX then

A

BYBX\frac{B_{Y}}{B_{X}} = 1

B

BYBX\frac{B_{Y}}{B_{X}} = 2

C

BYBX\frac{B_{Y}}{B_{X}} = 12\frac{1}{2}

D

BYBX\frac{B_{Y}}{B_{X}} = 14\frac{1}{4}

Answer

BYBX\frac{B_{Y}}{B_{X}} = 12\frac{1}{2}

Explanation

Solution

By = µ0NI(2r)22[(2r)2+d2]3/2\frac{µ_{0}NI(2r)^{2}}{2\lbrack(2r)^{2} + d^{2}\rbrack^{3/2}}

Bx = µ0NI(r)22[r2+(d/2)2]3/2\frac{µ_{0}NI(r)^{2}}{2\lbrack r^{2} + (d/2)^{2}\rbrack^{3/2}}

Ž ByBx\frac{B_{y}}{B_{x}} = 12\frac{1}{2}