Two concentric coils each of radius equal to `2 pi cm` are placed at right angles to each other ` 3 ampere and 4 ampere` are the currents flowing in each coil respectively. The magnetic induction in `weber//m^(2)` at the centre of the coils will be
`( mu_(0) = 4 pi xx 10^(-7) Wb// A.m)`

Options

A. `12xx10^(-5)`
B. `10^(-5)`
C. `5xx10^(-5)`
D. `7xx10^(-5)`

Answer

C

Explanation

Magnetic field at P, `B_(1)=(mu_(0)I_(2))/(2R)`
`=(4pixx10^(-7)xx4)/(2xx0.02pi)=4xx10^(-5)Wb//m^(2)`

Magnetic field, at Q,
`B_(2)=(mu_(0)I_(1))/(2R)=(4pixx10^(-7)xx3)/(2xx0.02pi)=3xx10^(-5)Wb//m^(2)`
`therefore" "B=sqrt(B_(1)^(2)+B_(2)^(2))`
`=sqrt((4xx10^(-5))+(3xx10^(-5))^(2))=5xx10^(-5)Wb//m^(2)`