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

3

Explanation

`B_(P)=(mu_(0)l_(2))/(2R)`
`=(4pixx10^(-7)xx4)/(2xx0.02pi)=4xx10^(-5)Wb//m^(2)`
`B_(Q)=(mu_(0)l_(1))/(2R)`
`=(4pixx10^(-7)xx3)/(2xx0.2pi)=3xx10^(-5)Wb//m^(2) rArr :.B=sqrt(B_(P)^(2)+B_(Q)^(2))`
`sqrt((4xx10^(-5))^(2)+(3xx10^(-5))^(2))=5xx10^(-5)Wb//m^(2)`