A long wire carries a current of `20A` along the directed axis of a long solenoid. The field due to a solenoid is `4mT`. Find the resultant field at a point `3mm` from the solenoid axis.

Answer

`4*2mT`; `18*4^@` with the directed axis

Explanation

the magnetic field due to current through solenoid, `vecB_s` is directed parallel to the axis of wire where `B_S=4mT`. The magnetic field due to current through straight wire is in the form of concentric circular magnetic lines of force. On one circular magnetic line of force, the magnetic field induction at all points is same in magnitude. The magnetic field induction due to current through straight wire at a perpendicular distance `r(=3mm)` is

`B_w=(mu_0)/(4pi)(2I)/(r)`. It is acting `_|_r` to `vecB_s`
`=(10^-7xx2xx20)/(3xx10^-3)=1*33xx10^-3T=1*33mT`
The resultant magnetic field induction at P in magnitude
`B=sqrt(B_S^2+B_w^2)=sqrt(4^2+(1*33)^2)=4*2mT`
`tantheta=(1*33)/(4)=tan18*4^@`
or `theta=18*4^@` with the directed axis.