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) → \( \displaystyle\frac{\mu_0 I}{\sqrt{2}R} \)
The magnetic field at the centre of a circular loop is directed along the axis of the loop, perpendicular to its plane.
\( \displaystyle B = \frac{\mu_0 I}{2R} \)
Both loops have the same \( I \) and \( R \), so each gives a field of this size at O. The loops lie in perpendicular planes, so their axes, and hence the two fields, are perpendicular to each other. The net field is their vector sum:
\( \displaystyle B_{\mathrm{net}} = \sqrt{B^{2} + B^{2}} = \sqrt{2}\,B = \sqrt{2}\,\frac{\mu_0 I}{2R} \)
\( \displaystyle B_{\mathrm{net}} = \frac{\mu_0 I}{\sqrt{2}R} \)