A circular loop of radius R carries a steady current I₁ . A very long, straight wire carrying a steady current I₂ is placed in the same plane, tangent to the circular loop and insulated from it. If the net magnetic field at the center of the circular loop is zero, what is the ratio of the currents I₁ I₂ ?

Step-by-step solution

The magnetic field at the center of the circular loop due to its own current I₁ is: B₁ = ₀ I₁ 2R The long straight wire is tangent to the loop, so its perpendicular distance from the center is R . The magnetic field at the center due to the straight wire carrying current I₂ is: B₂ = ₀ I₂ 2 R For the net magnetic field at the center to be zero, the two magnetic fields must be equal in magnitude and opposite in direction. Equating their magnitudes gives: ₀ I₁ 2R = ₀ I₂ 2 R Rearranging the terms to find the ratio I₁ I