Imagine looking at a solenoid from above. Current passing is through it in a clockwise direction. The direction of the field lines therefore is towards the bottom of the solenoid.
Now pass a straight current carrying wire through the central axis of the solenoid. The current in the wire is travelling in a downward direction so the field around it is going in a clockwise direction if viewed from above.
My question now is how do the field lines interact, and is there any resultant force on the wire?
My attempt at thinking this through says that the field lines of the solenoid and wire will become downward spiralling field lines.
Using this I believe that the wire will experience force in the upward direction.
Is this correct?
Best Answer
The magnetic field created by the wire is azimutal while the field created by the solenoide can be studied as the sum of two contributions. The first one is an uniform longitudinal field inside the solenoid and the second is an azimutal field outside the solenoid that varies as I/r. Therefore the magnetic force the wire experiences is null because current and B are parallel or because the current does not see the field. Alternatively you can analize the magnetic force the solenoid experiences. The current on it has two components. The horizontal component does not sense force because it is parallel to B field. The vertical is attracted by the central wire, but after integrate the total force will be zero by symmetry considerations.