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

Answer

C

Explanation

(c ) `B_(P) = (mu_(0) I_(2))/(2R)`
`= (4 pi xx 10^(-7) xx 4)/(2 xx 0.02 pi) = 4 xx 10^(-5) Wb//m^(2)`
`B_(Q) = (mu_(0) I_(1))/(2R) = (4 pi xx 10^(-7) xx 3)/(2 xx 0.02 pi) = 3 xx 10^(-5) Wb//m^(2)`
`= :. B = sqrt(B_(P)^(2) + B_(Q)^(2))`
`= sqrt((4 xx 10^(-5))^(2) + (3 xx 10^(-5))^(2))`
`= 5 xx 10^(-5) Wb//m^(2)`