Correct statement about solenoid

[songoku]

Homework Statement

A long solenoid with closely spaced turns carries a direct electric current. Each turn of wire exerts ....
(A) an attractive force on the next adjacent turn.
(B) a repulsive force on the next adjacent turn.
(C) zero force on the next adjacent turn.
(D) either an attractive or a repulsive force on the next adjacent turn, depending on the direction of current in the solenoid.
(E) either an attractive or a repulsive force on the next adjacent turn, but is not depending on the direction of current in the solenoid.

Relevant Equations

Fleming Left hand rule

Right hand grip rule

I imagine the question to be like this:

Take x - axis as horizontal and y - axis as vertical so the cross sectional area of the solenoid is parallel to x - y plane, then I take two parallel circles (back to back) to represent "A long solenoid with closely spaced turns".

I assume there is clockwise current flowing through the first circle (the front one) so there will also be clockwise current flowing through second circle (behind the first circle). Based on right hand grip rule, there will be magnetic field directed into the plane (cross)

Now I take small section at the top part of second circle so it can be considered a straight wire. This wire will have current flowing to the right and magnetic field directed into the plane so by using fleming left hand rule, there will be magnetic force directed upwards.

Doing the same for the bottom section of second circle, the direction of force will be downwards so this will cancel out the force acting on top section and same thing happens to all part of the circle.

My answer is (c) but the answer key is (a). Why there is attractive force between adjacent turns? Thanks

 

[Delta2]

Based on right hand grip rule, there will be magnetic field directed into the plane (cross)

This is you main assumption in which you base all your reasoning but while it is true in the region towards the center of the loops it is not true in the region between adjacent segments of the wire of the loops(i mean in the region between the wires that make up adjacent loops, hard to explain this without a figure). The magnetic field in this "in-between region" is quite different and its field lines resemble those of a magnetic field of a straight conductor.

To see how the force is attractive take a small segment $dl_1$ in one loop and find the force that exerts in the ""corresponding parallel "" $dl_2$ in the adjacent loop. You can treat $dl_1$ and $dl_2$ as straight pieces of wire and find the force that two straight pieces of wire exert on each other with current in the same direction.

 

[songoku]

This is you main assumption in which you base all your reasoning but while it is true in the region towards the center of the loops it is not true in the region between adjacent segments of the wire of the loops(i mean in the region between the wires that make up adjacent loops, hard to explain this without a figure). The magnetic field in this "in-between region" is quite different and its field lines resemble those of a magnetic field of a straight conductor.

To see how the force is attractive take a small segment $dl_1$ in one loop and find the force that exerts in the ""corresponding parallel "" $dl_2$ in the adjacent loop. You can treat $dl_1$ and $dl_2$ as straight pieces of wire and find the force that two straight pieces of wire exert on each other with current in the same direction.

I think I get it. Thank you very much Delta2