Two concentric but mutually perpendicular conduction coils are carrying current 3A and 4A, respectively . if the radius of each coil be `2pi,cm`. What will be the magnetic induction at the centre of the coils ?
`(mu_(0)=4pixx10^(-7)Wb*A^(-1)m^(-1))`.

Explanation

`r=2pi cm =(pi)/(50) m`
Magnetic field at the centre of circular coil , `B=(mu_(0)I)/(2r)`
`:.` For the first coil,
`B_(1)=((4pixx10^(-7))xx3)/(2xx(pi)/(50))=3xx10^(-5)Wb*m^(-2)`
and for the second coil,
`B_(2)=((4pi xx10^(-7))xx4)/(2xx(pi)/(50))=4xx10^(-5)Wb *m^(-2)`
Since the coils are mutually perpendicular `B_(1) and B_(2)` are also at right angles to each other. Hence the resultant magnetic field,
`B=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt((3)^(2)+(4)^(2))xx10^(-5)`
`=5xx10^(-5)Wb*m^(-2)`