Circular loop of a wire and a long straight wire carry currents I_c and I_e respectively as shown in figure. Assuming that these are placed in the same plane, the magnetic field will be zero at the centre of the loop when separation H is

Step-by-step solution

Magnetic field due to a circular loop at the centre of the loop is B₁= ₀ 4 2 I_c R . Magnetic field due to a straight line at the centre of the loop is B₂= ₀ 2 I_e 4 H Both these fields act in opposite direction hence total magnetic field at the centre of the loop is aligned & B=B₁-B₂= ₀ 2 I_c 4 R - ₀ 2 I_e 4 H & B=0 (given). & ₀ 2 I_c 4 R = ₀ 2 I_e 4 H or, H= I_e R I_c . aligned