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

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Question

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

A

9.1 × 10^–11 weber

B

3.3 × 10^–11 weber

C

6 × 10^–11 weber

D

6.6 × 10^–9 weber

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$B = \frac{µ_{0} {ia}^{2}}{2 {(a^{2} + x^{2})}^{3 / 2}}$

$B = \frac{4 π \times 10^{- 7} \times i {(0 .2)}^{2}}{2 (1 .5625 \times 10^{- 2})}$

$ϕ = BA = \frac{4 π \times 10^{- 7} \times 0 .04}{2 (1 .5625 \times 10^{- 2})} \times π {(0 .0 3)}^{2}$

= 4.6 × 10^–6 × 10^–7 × 10² = M¹²

= 4.6 × 10^–11

M₁₂ = M₂₁

$ϕ$ = 4.6 × 10^–11 × 2 = 9.2 × 10^–11 weber

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