Two concentric coils each of radius equal to `2pi` cm are placed at right angles to each there. 3 A and 4 A are the currents flowing in each coil respectively.
The megnetic induction in `Wb//m^(2)` at the centre of the coil will be `(mu_(0) =4pi xx10^(-7)Wb//Am)`

Options

A. `12 xx 10^(-5)`
B. `10^(-6)`
C. `5 xx 10^(-5)`
D. `7 xx 10^(-5)`

Answer

C

Explanation

`B_(p) = (mu_(0) I_(2))/(2R)`
`= (4pi 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)`
`therefore 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)`