# Would a conical-shaped solenoid be propelled by its interaction with the Earth's magnetic field?

I am wondering if the interaction between the magnetic field created by a conical-shaped solenoid and the Earth's magnetic field will result in this conical-shaped solenoid being propelled through the Earth's atmosphere.

I am planning to build such a solenoid and then I plan to mount it on a small raft which I will build to see if the raft will be propelled across the water by this solenoid.

This solenoid will be a hollow cone made out of plastic and will have an electrified wire wrapped around it. I am planning to use a plastic cone in which the larger end will be 41cm in diameter and the smaller end will be 10cm in diameter. The power source will be either a battery pack placed on the raft, or perhaps via wires coming from a DC power supply.

I am thinking that when this conical-shaped solenoid is pointed towards the North Pole, with the smaller opening of the cone pointed towards the North Pole, the Earth's magnetic field within the interior of this solenoid will interact with the magnetic field of the solenoid. Due to this interaction, the solenoid (and the raft) will be propelled towards the North Pole. This working principle is based off of the interaction of two current carrying wires shown in the drawing below.

This drawing is from: https://www.physics.louisville.edu/cldavis/phys111/notes/magn_forces_curr.html

Changing the polarity of the solenoid should result in the solenoid be propelled towards the South Pole.

I created a drawing which shows a cross-sectional view of how the magnetic field of this solenoid and the Earth's magnetic field should interact with each other:

Before I put in the time and effort to build this test model, I would like to know if this working principle is a sound one or if this test model will not work due to me misunderstanding something.

Would a conical-shaped solenoid be propelled by its interaction with the Earth's magnetic field?

• By your logic, why wouldn't a cylindrical solenoid (or a permanent magnet) work in the same way? What is special about the conical shape ?
– AJN
Oct 8, 2023 at 2:57
• @AJN, today I realized that my hypothesis about this conical-shaped solenoid is wrong and thus that it won't produce any thrust/propulsion. Oct 9, 2023 at 0:04

I think you'll be very disappointed.

Figure 1. Image source: Science Class.

Your coil will form a very weak magnet since it has an air core. (A good solenoid will use an iron core as it has a permeability 1000 times that of air.)

Place your solenoid on a boat and it will rotate so that it's north pole will point north. (The Earth's north pole is actually a magnetic south pole! That's why the magnet's north pole points in that direction.) Once that happens the turning moment will fall to zero and the forces will be balanced with the same force pulling north and south.

I think you'll be making a battery powered compass - and a very weak one.

• @ Transistor, I agree with you that the solenoid will act as a compass and will rotate itself, along with the raft, so that it's north pole will point north. Yet, after it is done rotating the raft, I believe that the continued interaction between the solenoid's magnetic field with the Earth's magnetic field will result in the raft being propelled through the water towards either the North or the South Pole, depending on the polarity of the solenoid. Oct 7, 2023 at 21:54
• Why? Why would it be attracted to the north pole in preference to the south pole or vice versa? Do you think the floating compass needle would move? Why? Oct 7, 2023 at 21:58
• Tip: To ping another user you use @username with no spaces after the @ or in the username. I didn't get a ping from your comment. Oct 7, 2023 at 22:00
• well, the way I see it is that it goes back to the working principle of how two current carrying wires interact with one another. Also, sorry about not using the proper naming format... I just wanted to make sure that my comment(s) are meant for you and not for someone else if other people choose to reply in this thread of your answer. Oct 7, 2023 at 22:02
• But in your own diagram the forces on the wires are at right angles to the lines of flux and opposing each other. Since your wires are on a former they can't move relative to each other and the net force left to right is zero. There is no force in the top to bottom direction either. Oct 7, 2023 at 22:51