Question

Two identical coils carry equal currents have a common centre and their planes are at right angles to each other. The ratio of the magnitude of the resultant magnetic field at the centre and the field due to one coil is :

• A. $2:1$
• B. $1:2$
• C. $\sqrt{2}:1$
• D. $1:\sqrt{2}$

Answer 1

The correct option is C $\sqrt{2}:1$

The magnetic field due to each coil is equal in magnitude and perpendicular to each other

Let magnetic field due to one of them be B

Then the resultant magnetic field due to 2 coil = $\sqrt{B^2+B^2}=\sqrt{2}B$

The ratio of the magnitude of the resultant magnetic field at the centre and the field due to one coil = $\sqrt{2}B:B=\sqrt{2}:1$