Two small circular loops, marked (1) and (2), carrying equal currents are placed with the geometrical axes perpendicular to each other as shown in figure. Find the magnitude and direction of the net magnetic field produced at the point O.

Explanation

The magnetic field at a point on the axis of current carrying circular loops (1) and (2) is given by
`B_(1) = B_(2) = (mu_(0)Ia^(2))/(2(a^(2) + x^(2))^(3//2))`
Where a = radius of loop
The direction of magnetic field at O due to loops (1) and (2) and the resultant magnetic field is shown below:

The resultant magnetic field is given by:
`B_("net") = sqrt(B_(1)^(2) + B_(2)^(2)) = sqrt2 (mu_(0)Ia^(2))/(2(a^(2) + x^(2))^(3//2)) = (mu_(0)Ia^(2))/(sqrt2 (a^(2) + x^(2))^(3//2))`