Two indentical circular coils, P and Q each of radius R, carrying currents 1A and `sqrt(3)A` resepectively. Are placed concentrically and perpendicular to each other laying in the XY and Yz planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.

Explanation

Field due to current in coil P is `vecB_(1)=(mu_(0)I_(1))/(2R)*hatk`
Current in coil Q is `vecB_(2)=(mu_(0)I_(2))/(2R)*hati`
Net field `vecB=vecB_(1)+vecB_(2)`
`vecB=((mu_(0)I_(1))/(2R)) hatk+((mu_(0)I_(2))/(2R))hati`
`=((mu_(0))/(2R))hatk+ ((sqrt(3)mu_(0))/(2R))hat i( . I_(1)=1A, I_(2) sqrt(3)A)`
`|vecB|= sqrt(((mu_(0))/(2R))^(2)+((sqrt(3)mu_(0))/(2R))^(2))=(mu_(0))/(2R) sqrt(1+3)=(mu_(0))/(2R)xx2`
`:. |vecB|=(mu_(0))/(R)`
The resultant magnetic field is directed in XY-plane.