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Q.

An otherwise infinite, straight wire has two concentric loops of radii a and b carrying equal currents in opposite directions as shown in figure. The magnetic field at the common center is zero for

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a

$\frac{a}{b} = \frac{π - 1}{π}$

b

$\frac{a}{b} = \frac{π - 1}{π + 1}$

c

$\frac{a}{b} = \frac{π}{π + 1}$

d

$\frac{a}{b} = \frac{π + 1}{π - 1}$

answer is B.

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Detailed Solution

$B_{centee} = 0 \frac{μ_{0} I}{4 π b} ⊙ + \frac{μ_{0} I}{4 π b} ⊙ + \frac{μ_{0} I}{2 b} ⊙ + \frac{μ_{0} I}{2 a} \otimes = 0 \Rightarrow \frac{μ_{0} I}{2 π b} + \frac{μ_{0} I}{2 b} - \frac{μ_{0} I}{2 a} = 0 \Rightarrow \frac{1}{2 π b} + \frac{1}{2 b} = \frac{1}{2 a} \Rightarrow \frac{a}{b} = \frac{π}{π + 1}$

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An otherwise infinite, straight wire has two concentric loops of radii a and b carrying equal currents in opposite directions as shown in figure. The magnetic field at the common center is zero for