A circular loop of radius r carries current i. A long straight wire carrying 4i is placed in the loop's plane so the field at the centre is zero. If the wire-centre distance is xr/π, find x.
Physics · Magnetic effect of current
JEE Mains

Question

A circular loop of radius r carries current i. A long straight wire carrying 4i is placed in the loop's plane so the field at the centre is zero. If the wire-centre distance is xr/π, find x.

G1 Physics · Accepted Answer

Loop field is μ₀i/(2r). Straight-wire field is μ₀(4i)/(2πd). Equating gives d=4r/π. Therefore x=4.