Two circular coils are made of the same wire. The radius of coil 1 is twice the radius of coil 2. In what ratio should potential differences be applied across them to make the magnetic fields at their centres equal?
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Question

Two circular coils are made of the same wire. The radius of coil 1 is twice the radius of coil 2. In what ratio should potential differences be applied across them to make the magnetic fields at their centres equal?

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G1 Physics · Accepted Answer

Step 1: At the center of a single circular coil, B=μ₀I/(2r). For identical wire thickness/material, coil resistance R(wire) ∝ length ∝ r. Step 2: To produce equal B at radii r₁=2r₂, currents must satisfy I₁/I₂=r₁/r₂=2. Step 3: With I=V/R(wire) and R₁/R₂=2, voltage ratio V₁/V₂=(I₁/I₂)(R₁/R₂)=2×2=4. Final C. Final answer: (C) 4.