In the figure are shown two long parallel current carrying wires I and II. Find the magnitudes and directions of the magnetic field induction at the point P, Q and R in the plane of paper.

Answer

`2xx10^-5T_|__r` to the plane of paper upwards; `10^-4T_|__r` to the plane of paper downwards; `4*7xx10^-5T_|__r` to the plane of paper upwards

Explanation

Resultant magnetic field induction at P is
`B=B_1-B_2`
`=(mu_0)/(4pi)(2I_1)/(r_1)-(mu_0)/(4pi)(2I_2)/(r_2)=(mu_0)/(4pi)xx2[I_1/r_1-I_2/r_2]`
Here, `I_1=20A, r_1=0*1m`,
`I_2=30A`, `r_2=0*30m`
`B=10^-7xx2[(20)/(0*1)-(30)/(0*3)]=2xx10^-5T` It will be acting perpendicular to the plane of paper upwards.
Resultant magntic field induction at Q is
`B=(mu_0)/(4pi)xx2[(20)/(0*1)+(30)/(0*1)]`
`=10^-7xx2xx500=10^-4T`
It will be acting perpendicular to the plane of the paper downwards.
Resultant magntic field induction at R is
`B=(mu_0)/(4pi)xx2[(30)/(0*1)-(20)/(0*3)]=4*7xx10^-5T`
It will be acting perpendicular to the plane of the paper upwards.