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 the bigger loop is?

As field due to current loop 1 at an axial point B₁ = μ₀I₁R₂²/2(d²+R₂²)³/², Flux linked with smaller loop 2 due to B₁ is Φ₂ = B₁A₂ = μ₀I₁R₂²πr₂²/2(d²+R₂²)³/². The coefficient of mutual inductance between the loops is M = Φ₂/I₁ = μ₀R₂²πr₂²/2(d²+R₂²)³/². Flux linked with bigger loop 1 is Φ = MI₂ = μ₀R₂²πr₂²I₂/2(d²+R₂²)³/². Substituting the given values, we get Φ₁ = 4π×10⁻⁷×(20×10⁻²)²×π×(0.3×10⁻²)²×2/2[(15×10⁻²)²+(20×10⁻²)²]³/²