# Does a current-carrying wire running through the centre of a solenoid experience force?

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?

• What force does the wire experience if it's not carrying current? Commented Jan 22, 2014 at 14:30

## 2 Answers

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.

It seems you are asking about the force on wire running along the axis of a solenoid. The answer is that there is no magnetic force on the wire. The force on a wire is the cross product of the current thru it and the magnetic field it is in. In your case, both are parallel and the cross product is therefore zero.

Put another way, for a wire to experience magnetic force due to current thru it, that wire has to be perpendicular to the magnetic field lines. You have it parallel.

• I'd add the constraint that the wire is essentially symmetric w.r.t. the solenoid (extending to infinity along the axis). If the wire is bent at right angles just past one end of the solenoid, it's a little like placing an iron slug half-way into the solenoid- the asymmetric fieldlines on the slug will pull it into the coil. (poor analogy but I hope you see my concern) Commented Jan 22, 2014 at 15:54