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Q.

The coils $C_{1}$ and $C_{2}$ have same number of turns and carry equal currents in the same sense. They subtend the same angle $θ$ at P. If the magnetic field produced by $C_{1}$ at P is B, then effective magnetic field that produced due to both $C_{1} a n d C_{2}$ will be

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a

$\frac{B}{3 \sqrt{2}}$

b

B/2

c

2B

d

3B

answer is A.

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Detailed Solution

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$M a g n e t i c F i e l d a t a p o i n t o n a x i s, B = \frac{μ_{o} i R^{2}}{2 {(R^{2} + x^{2})}^{3 / 2}}^{B} C_{1} = B = \frac{μ_{0} i R^{2}}{2 {[R^{2} + {(2 R)}^{2}]}^{3 / 2}} = \frac{μ_{0} i}{2 R {(1 + 4)}^{3 / 2}}^{B} C_{2} = B_{2} = \frac{μ_{0} i {(R / 2)}^{2}}{2 {[{(\frac{R}{2})}^{2} + R^{2}]}^{3 / 2}} = \frac{μ_{0} i}{2 \frac{R}{2} {(1 + 4)}^{3 / 2}} = 2 B ∴ E f f e c t i v e B a t = B + 2 B = 3 B$

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