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. `(mu_(0) I)/(R)`
B. `(sqrt(5 mu_(0) I))/(2R)`
C. `(3mu_(0) I)/(2R)`
D. `(mu_(0) I)/(2R)`

Answer

B

Explanation

The magnetic field `(B)` at the centre of circular current carrying coil of radius `R` and current `I, B = (mu_(0) I)/(2R)`
Similarly, if current `= 2l`, then
Magnetic filed `= (mu_(0) 2 I)/(2R) = 2B`
So, reusltant magnetic field
`= sqrt(B^(2) + (2B)^(2)) = sqrt(5B^(2)) = sqrt((5B)`
`= (mu_(0) I sqrt(5))/(2R)`