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 is in an anticlockwise direction. So the magnetic field (B_P) will be in the direction shown.

Similarly, in Q the direction of magnetic field B_Q will be shown (from Flemings left-hand rule) the resultant of B_P and B_Q will be B.

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

B_P = B_Q

because both the coil has the same current and the same radius.

`B = sqrt(B_P^2 + B_P^2) = sqrt2B_P`

∵ `B_P = (mu_0I)/(2R)`

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

⇒ B = `(mu_0I)/(sqrt2R)`

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