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

Options

A. `(sqrt(5)mu_0I)/(2R)`
B. `(3 mu_0I)/(2R)`
C. `(mu_0I)/(2R)`
D. `(mu_0I)/(R)`

Answer

A

Explanation

It acts in vertically upward direction.
As `B_1` and `B_2` are perpendicular to each other , therefore the resultant magnetic field induction at the centre O is
`B_("net") = sqrt(B_1^2 + B_2^2) = sqrt(((mu_0 I)/(2R)) + ((mu_0 2I)/(2R))^2)`
`= (mu_01)/(2R) sqrt((1)^2 + (2)^2)= (sqrt(5)mu_0I)/(2R)`