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. `(sqrt(5)mu_(0)I)/(2R)`
B. `(2mu_(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)=(mu_(0)I)/R`
`B_(1)` is `bot^(ar) B_(2)`
`B_(0)=sqrt(B_(1)^(2)+B_(2)^(2))=(mu_(0)I)/Rsqrt(1/4+1)`
`(sqrt(5) mu_(0)I)/(2R)`