Two similar coils of radius `R` are lying concentriclaly with their planes at right angels to each other. The currents flowing in them are `I` and `2I` respectively. The resulant magntic field induction at the centre will be

Options

A. `(sqrt5mu_0I)/(2R)`
B. `(3mu_0I)/(2R)`
C. `(mu_0I)/(2R)`
D. `(mu_0I)/(R)`

Answer

A

Explanation

Here, in first coil current I is flowing.
So, mag. field due to this coil carrying current I at the centre `B_1=(mu_0I)/(2R)`
Now, mag. field due to other coil carrying current `2I`, at the centre `B_2=(mu_02I)/(2R)`
Now, resultant magnetic field `B=sqrt(B_1^2+B_2^2)`
`=sqrt(((mu_0I)/(2R))^2+((mu_(0)2I)/(2R))^2)=(mu_0I)/(2R)sqrt(1+4)=sqrt5(mu_0I)/(2R)`