Two identical circular loops P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre as shown in figure. The magnitude of the net magnetic field at the common centre is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{μ_0I}{\sqrt{2}R}$
Magnetic field at the center is,
$B = \frac{\mu_0I}{2R}$
$∴B_P=B_Q=\frac{\mu_0I}{2R}$
Also, these loops are perpendicular to each other because the loops are in perpendicular planes.
$B_{net}=\sqrt{{B_P}^2+{B_Q}^2}$
$=\sqrt{\left(\frac{\mu_0I}{2R}\right)^2+\left(\frac{\mu_0I}{2R}\right)^2}$
$=\frac{\mu_0I}{2R}\sqrt{2}=\frac{μ_0I}{\sqrt{2}R}$