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

Answer

`02.24`

Explanation

Magnetic field induction due to vertical loop at center O is
`B_1=(mu_02I)/(2R)hatj`
Now,
`B_"net"=sqrt(B_1^2+B_2^2)`
`=sqrt(((mu_02I)/(2R))^2+((mu_04I)/(2R))^2)`
`=(mu_0I)/(2R)sqrt((2)^2+(4)^2)`
`=sqrt20/2(mu_0I)/R`
`:. B_"net"=(2sqrt5)/2=2.24(mu_0I)/R`