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

Answer

D

Explanation

The magnetic field to circular coil , `B_1`
`=(mu_0i_l)/(2r)=(mu_0i_l)/(2(2pixx10^(-2)))=(mu_0xx3xx10^2)/(4pi)`
`B_2 =(mu_0i_2)/(2(2pixx10^(-2)))=(mu_0xx4xx10^2)/(4pi)`
`B=sqrt(B_1^2+B_2^2)=mu_0/(4pi).5xx10^2`
`implies B = 10^(-7)xx5xx10^2`
`implies B = 5xx10^(-5) Wb//m^2`