Question

Two identical circular loops P and Q, each of radius R carrying current I are kept in perpendicular planes such that they have a common centre O as shown in the figure.

Find the magnitude and direction of the net magnetic field at point O.

Answer 1

In the P coil, the current flows anticlockwise. So the magnetic field (B_P) will be in the direction shown.

Similarly, in Q, the direction of the magnetic field BQ will be shown (from Fleming's left-hand rule), and the resultant of BP and BQ will be B.

So `B = sqrt(B_P^2 + B_Q^2)`

B_P = B_Q = `(mu_0I)/(2R)`

Because both coils have the same current and the same radius.

`B_"net" = sqrt(B_P^2 + B_Q^2)`

∵ `B_P = (mu_0I)/(2R)`

`B = sqrt2((mu_0I)/(2R))`

⇒ B = `(mu_0Isqrt2)/(2R)`

The net magnetic field is oriented at 45° to both fields.