Re: Propulsion with Lorentz force

Hello Nick,

Thank you very much for your question. In order to solve it, we will need to make a good visualization what will happen. First, let's have a look at the Helmholz coils. A pair of Helmholz coils produce a fairly homogeneous magnetic field between them. Because we have two pairs, we get two magnetic fields. Without loss of generality, we can say one goes up, in the positive x-direction, and one goes to the right, in the positive y-direction. If they don't, we'll just walk around the problem until we face it at an angle where they do go up and left.

We now know the magnetic field of the Helmholz coils, and this magnetic field exerts a force on the current that goes into the wire loop. Let's assume the current in the loop transverses it clockwise; if it goes counter-clockwise, you can repeat the argument, but with the directions reversed.

The rectangular loop consists of 4 pieces of wire. The top piece has a current going to the right, in the y-direction. The Lorentz force exerted is given by F = I B l, with F the Lorentz force, B the magnetic field strength, I the current and l the length of the piece of wire. The boldface means we are talking about vectors. The x is not a normal multiplication either, it is the so-called cross product. This means we multiply the magnitude of the vectors, but that the direction of the resulting vector is dependent on the direction of the vectors via the right-hand rule. The right-hand rule means that if we let the the current go through our right hand, and extend our fingers into the direction of the magnetic field, our thumb points in the direction of the Lorentz force. For the top left piece, we have a Lorentz force that points in the z-direction. The field that is parallel to the current produces no Lorentz force.

On the bottom end is another piece of wire, which is identical, apart from the fact the current goes in the opposite direction. This means we have a Lorentz force going in the negative z-direction, countering the Lorentz force at the top. Something Similar happens with the left and right part of the loop: the forces cancel. Hence, there is no net force available for propulsion.

However, the opposing pieces of wire do exert a torque, a force times a lever arm. The top part wants to go up, the bottom part wants to go down, like a spinning wheel. This torque can be used to let the wire loop spin, along a line that goes from the bottom left to the top right. In fact, this is the principle of the electric motor, and yes, these are very frequently used for propulsion.

So, in fact, this device does not move itself, as you already suggested in the question, but it can, and very frequently is, used for propulsion. Hope this helps.

Regards,

Bart Broks.