A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centers is 15 cm. If a current of 2.0 A flows through the bigger loop, then the flux linked with smaller loop is

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$6.6 \times 10^{- 9} W b$

$9.1 \times 10^{- 11} W b$

$3.3 \times 10^{- 11} W b$

$6 \times 10^{- 11} W b$

answer is A.

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Detailed Solution

Magnetic field at the centre of a small loop $B = \frac{μ_{0} I R_{2}^{2}}{2 {(R_{2}^{2} + x^{2})}^{3 / 2}}$

Area of smaller loop $S = π R_{1}^{2}$

Flux through smaller loop = BS

$\begin{array}{rcl} = & \frac{π μ_{0} I R_{1}^{2} R_{2}^{2}}{2 {(R_{2}^{2} + x^{2})}^{3 / 2}} \\ \Rightarrow & ϕ = 9.1 \times 10^{- 11} W b \end{array}$

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