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

Explanation

We know that the magnetic field at a point on the axial line of a small current loop of radius R is given by
`B = (mu_0 I R^2)/(2 x^3)`
`:.` Magnetic field at point O due to current loop number 1
`B_1 = (mu_0 I R^2)/(2x^3) ` along + ve X - axis.
and magnetic field at point O due to current loop number 2
`B_2 = (mu_0 I R^2)/(2 x^3) ` along + ve Y-axis
As `B_1 and B_2` are in mutually perpendicular directions (fig.) , the resulatant magnetic field subtends an angle B from horizontal, where
`tan beta = (B_2)/(B_1) = 1 implies beta = 45^@`