Two similar coils A and B of radius ' r ' and number of turns ' N ' each are placed concentrically with their planes perpendicular to each other. If I and 2 I are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be:

Step-by-step solution

The magnetic field at the center of a circular coil of radius r with N turns carrying current I is given by B = ₀ NI 2r . For coil A with current I , the magnetic field is B_A = ₀ NI 2r . For coil B with current 2I , the magnetic field is B_B = ₀ N(2I) 2r = 2 ₀ NI 2r = ₀ NI r . Since the planes of the coils are perpendicular to each other, the magnetic field vectors B _A and B _B are perpendicular to each other. The net magnetic induction B_ net is given by the vector sum B_ net = B_A^2 + B_B^2 . B_ net = ( ₀ NI 2r