2012 AIPMT-PRE Moving Charges and MagnetismMagnetic Field due to a Circular Coil Easy Question 9 of 15 in Magnetic Field due to a Circular Coil

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be

A $\frac{\mu_0I}{R}$
B $\frac{\sqrt5\mu_0I}{2R}$
C $\frac{3\mu_0I}{2R}$
D $\frac{\mu_0I}{2R}$

The answer is B.

Solution

Field at the centre of each coil: $B_1 = \frac{\mu_0I}{2R}$ and $B_2 = \frac{\mu_0(2I)}{2R}$
The planes are perpendicular, so the two fields are perpendicular to each other.
$B = \sqrt{B_1^2 + B_2^2} = \sqrt{\left(\frac{\mu_0I}{2R}\right)^2 + \left(\frac{2\mu_0I}{2R}\right)^2} = \frac{\sqrt5\mu_0I}{2R}$

Concept Resultant of perpendicular fields

Magnetic Field due to a Circular Coil in past papers

15 questions from this chapter have appeared across 12 exam years.