Two infinitely long straight conductors are arranged to be perpendicular to each other at a distance d = 0.02 m . Find the magnetic flux density at the mid-point of the separation. [Take,`i_(1)=2A and i_(2)=3A`]

Explanation

Magnetic field due to a current carrying conductor is given by
`B=(mu_(0))/(4pi) xx (2I)/(a)`
In wire carrying current `I_(1)` is
`B_(1)=(mu_(0))/(4pi) xx (2i_(1))/(a)=(10^(-7) xx 2 xx 2)/(0.01)" " ["Here, "i_(1)=2A, a=0.01m]`
`=4xx10^(-5)T`
In wire carrying current, `i_(2)` is
`B_(2)=(mu_(0))/(4pi) xx (2i_(2))/(a) =(10^(-7) xx 2 xx 3)/(0.01) " "["Here, " i_(2)=3A, a=0.01m]`
`=6xx 10^(-5)T`
Resultant magnetic flux density at mid-point will be
`=sqrt((4xx10^(-5))^(2) +(6xx10^(-5))^(2))`
`=7.2 xx 10^(-5)T`