Two identical loops P and Q each of radius 5cm are lying in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils, if they carry currents equal to 3A and 4A respectively.

Radius of each coil R=5cm=0.05m
Magnetic field produced by coil P and Q is B1 and B2 in x and y direction, respectively.
Magnetic field produced by coil P, B1 = μoI1/2R Tesla^x
∴B1 = (3μo)/2(0.05) = 30μo Tesla^x
Magnetic field produced by coil Q, B2 = μoI2/2R Tesla^y
∴B2 = (4μo)/2(0.05) = 40μo Tesla^y
Total magnetic field produced at the center B = √(B1^2 + B2^2)
∴B = √((30μo)^2 + (40μo)^2) ⇒B = 50μo Tesla
Direction of magnetic field tanθ = B2/B1
∴tanθ = 40μo/30μo = 4/3
⇒θ = tan⁻¹(4/3) = 53o