Two coils P and Q each of radius R carry currents I and 8 I respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( ₀= permeability of free space)

Step-by-step solution

Magnetic field at the centre of P due to its current I is B _ p = ₀ I 2 R ...(i) Magnetic field at the centre of Q due to its current 8 1 is aligned & B _ Q = ₀ 8 I 2 R ...(ii) & ~B _ net [From(i) and (ii)] & = B _ p ^2+ B _ Q ^2 & = ( ₀ I 2 R )^2+ ( ₀ 8 I 2 R )^2 & = 3 ₀ I 2 R aligned