Two identical circular wires P and Q each of radius R and carrying current ‘I’ are kept in perpendicular planes such that they have a common center as shown in the figure. Find the magnitude and direction of the net magnetic field at the common center of the two coils. 

Coils P and Q each of radius R have a common centre:

B_P is directed vertically upwards and B_Q is directed horizontally.

Therefore, resultant magnetic field is given by,


We have,



This is the required of the resultant magnetic field. 

Direction of magnetic field is given by, 


The resultant magnetic field is directed at angle of 45° with either of the fields.