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. `(sqrt5 mu_(0)I)/(2R)`
B. `(3 mu_(0) I)/(2R)`
C. `(mu_(0) I)/(2R)`
D. `(mu_(0) I)/(R )`

Answer

A

Explanation

`B_(1) = (mu_(0) I)/(2R) , B_(2) = (mu_(0) (2I))/(2R)`
`B_("net") = sqrt(B_(1)^(2) + B_(2)^(2))`
`= (mu_(0) I)/(2R) sqrt5`