Find the magnetic energy stored in the system of two concentric loops of radii r and R(Rr).If the loopss have currents of same magnitude i₀ .Ignore the effect of self inductance.Ans={(pie)(mu)₀ (ri₀ )² }/2R

From the theory of mutual induction we know that magnetic energy stored between two conductors carrying is given by

U = Mi₁i₂

 Here i₁ = i₂ = i₀

U = Mi₀²

  = (Mi₀)i₀

  = Φ₁₂i₀  ---1.

Φ₁₂ = BA

Here B = magnetic field passing through coil 2

B originates due to current i₁ in coil 1

B = μ₀i₀/2R

Flux linked originating due to coil 1 linking 2 will be

Φ₁₂  = BA = (μ₀i₀/2R)πr²

By eqn. 1

U = (μ₀i₀/2R)πr² i₀

  = π μ₀r²i₀²/2R