Two circular coils 1 and 2 are made from the same wire but the radius of the 1^ st coil is twice that of the 2^ nd coil. What potential difference in volts should be applied across them so that the magnetic field at their centres is the same?

Step-by-step solution

Let r₁ and r₂ be the radius of coil 1 and coil 2 . If B₁ and B₂ are magnetic induction at their centre then B₁= ₀ I₁ 2 r₁ and B₂= ₀ I₂ 2 r₂ B₁=B₂ and r₁=2 r₂ there I₁=2 I₂ Again if R₁ and R₂ are resistance of the coil 2 then R₁=2 R₂ (as R length =2 r) and if v₁ and v₂ are the potential difference across them respectively then aligned V₁ V₂ & = I₁ R₁ I₂ R₂ & = (2 I₂ ) (2 R₂ ) I₂ R₂ =4 aligned