Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown.

Step-by-step solution

Suppose the magnetic field produced due to each coil is B . The two coils are kept perpendicular hence, the angle between these is 90^ therefore, the resultant magnetic field is given by aligned & = B^2+B^2+2 B B 90^ & = 2 B^2+2 B^2 0 & = 2 B^2 =B 2 aligned Hence, the ratio of magnetic field due to one coil and the resultant magnetic field is given by = B 2 B =1: 2