Circular loop of a wire and a long straight wire carry currents lc and
le, respectively as shown in figure. Assuming that these are placed in

the same plane. The magnetic fields will be zero at the centre of the

loop when the separation H is-

Using Ampere's circuital law. Mag. field at centre of circular coil due to long straight wire
B1=μ0Il2πHB1=μ0Il2πH
Due to circular coil, mag. field at the centre O is given byB2=μ0Ic2RB2=μ0Ic2R
NowB1B1andB2B2are is opposite directions. For resultant to be zero,B1=B2B1=B2
μ0Il2πH=μ0Ic2Rμ0Il2πH=μ0Ic2R, i.e.,H=IlRIcπ