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. `7xx10^(-5)`
D. `5xx10^(-5)`

Answer

D

Explanation

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

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