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

Answer

C

Explanation

Magentic field at the centre of circular current carrying coil of radius R and current I is `=(mu_(0)I)/(R )=B`
Magnetic field at the centre of circular current carrying coil of radius R and current 2I is `=(mu_(0)2I)/(2R)=2B`
The resulting magnetic field will be `=sqrt(B^(2)+4B^(2))=sqrt(5)B`