# Can Lenz's Law Allow a Simple Block of Metal to Divert a Charged Electron Beam?

I was curious about an odd effect I first saw in video here: YouTube : Copper's Surprising Reaction to Strong Magnets

In the video, a big heavy magnet is brought to an abrupt halt by a simple piece of copper. The effect is called Lenz's Law : an increase in the magnetic flux is created by the approaching magnet. The metal naturally resists the increasing magnetic flux by producing an almost equal and opposite magnetic field. The net effect is that the incoming magnet/projectile is halted before it can do harm.

Can Lenz's Law be applied to deflect or shield from beams of charged particles? From a world building perspective, could a primitive people fend off high-tech invaders armed with charged particle weapons by using metal to deflect the beam?

• Please note that science based and hard science are mutually exclusive. Pick one of the two.
– L.Dutch
Aug 21 '18 at 13:17
• (1) There is nothing special about copper. (2) It is not at all clear what you mean by "this" when you ask whether "this" can divert a plasma beam. (3) It is utterly unclear what you mean by a "plasma beam". Plasma, by its very nature, needs to be confined somehow or else it will rapidly expand away. Aug 21 '18 at 13:49
• @L.Dutch OP seems to propose not to use magnets or electronagnets, but simple copper plates, hoping that the moving plasma beam would induce currents strong enough that their magnetic field would disperse and decellerate the beam. Aug 21 '18 at 17:28
• I was working on an answer to this based on a torroidal plasma projectile, but there are many things I can't find data on: what does the induced magnetic field look like, how strong is it, how far does it extend, etc. Even for existing systems I can't find this data, and if I could it would obviously be different for a fictional system that can be used as a weapon, which makes it tricky to provide a hard-science answer. Turns out magneto-hydrodynamics is complicated. (And if the weapon is something like an electron beam, then no.) Aug 21 '18 at 20:39
• @realityChemist I was thinking something like an electron beam, but it's good to know about some other options. Aug 22 '18 at 17:16

Yes, but you would need to generate a really strong magnetic/electric field.

Plasma can produce its own magnetic field if it is observed during a time-frame in which there are electrical currents present. Another mechanism that could be used by plasma to generate a magnetic field would be the concept of "plasma instability." Plasma instability is when some form of free energy (any form of first law energy that can perform thermodynamic work, i.e thermal energy) is introduced into the system causing instability. The system will sometimes respond by converting that free energy into electromagnetic energy by releasing an electromagnetic wave.

Now normally the generated field would flow in all directions and cancel itself out, but assuming the plasma is being fired like a projectile in one direction, we can assume that all of the fields would follow the same direction and not cancel each other out. And lets assume that it's headed towards you.

What can I do about it?

By primitive, I assume you mean at least with modern human technological capabilities. Well if you wanted to deflect plasma, you would have to introduce a lot of energy into the plasma cloud flying at you. The best way to do this would be to point and fire a high-powered laser at the cloud, and wait for it to generate an electromagnetic field. Then you would have to be wearing some form of protective armor that creates a powerful magnetic field that moves in a direction to repel the magnetic field created by the plasma. Why powerful? You don't want any plasma touching you as it would probably be at least 1000 degrees C. So it would be best to repel it all as fast and as far away as possible. You'd probably then want neodymium or samarium-cobalt which are the two types of rare-earth magnets. However, they are extremely heavy with neodymium being the lighter of the two. With current human technology, it would be unfeasible to make a relatively cheap form of ultra-magnetic armor for a person to wear into battle against a plasma gun equipped alien race.

Lenz's Law

Rare-earth magnets aside, what about electromagnetism as described in Lenz's Law? Well all electromagnets operate on the principle that the more electromotive force(emf) A.K.A voltage is introduced, the stronger the magnetic field would be in the opposite direction of the original magnetic flux. What does this mean? It means that the more power, the stronger the repulsion/attraction. To achieve a similar repulsion to a 1 foot in diameter and 1 inch thick circular neodymium plate, of the lowest magnetic quality of neodymium, you would need to apply 409.278 Amps of current to an electromagnet coil made of copper with 500 turns. Why copper? Because it's the second most conductive metal behind the expensive silver. It is heavier than neodymium, but the advantage an electromagnet is that we don't have to use as much metal. We only need to wrap the armor with copper coils able to safely carry 450 Amps of current, which while still being heavy is about half as heavy as the 400 pounds of neodymium. But 410 Amps is a lot. And it's not cheap either, powering this armor for 12 hours a day in the U.S for every day for a year will run you \$90,570.31 for just one set of armor. And that's not to mention the cost of production. But if money is no object, then it is not only possible, but feasible in terms of combat.

Is there any way I can stretch this?

Fallout power armor is an example of how extremely heavy armor could be used for battle, but it's definitely not primitive as far as technology goes. If it is a more futuristic setting, then the possibility does arise for neodymium/heavy armor to be an option. However, while it might not be 100% suitable economically for single soldier use with modern technology, it could be used on a larger scale for buildings and even planets against alien invaders for a civilization with the same technological knowledge as humans. The inhabitants of the building/planet see the plasma flying towards them, so they use an even more powerful laser to bring the plasma bolt/cloud into instability, then using either an electromagnet or the planet's own magnetic field to deflect the plasma.

No Magnets

Without magnets it would be hard to deflect plasma as there isn't really any better options. Lenz's Law is directly tied to and helps describe the relationship between electricity and magnetism as originally proposed by Michael Faraday's law of induction. In a way, the plasma can charge the copper by introducing a current and making it an electromagnet for an extremely short period of time as the current would transfer, but by then it would be too late to save anything that someone was trying to protect. As again, plasma is hot, and would vaporize things once they got that close. Hypothetically, even if the copper wasn't vaporized by contact, the induced emf to the copper wouldn't produce enough magnetic force to push the plasma away, as if we follow the formula F = (n x i)2 x magnetic constant x a / (2 x g2) using the same dimensions of the electromagnet design I previously described, we would get a much lower repulsion on the plasma as unless the instability on the plasma was massive. However, given enough turns on the copper electromagnet, you could definitely use the charge on an unstable moving system of plasma to create an electromagnet powerful enough to repel it, but for a split second it is definitely still an electromagnet. This is of course assuming the coil itself isn't vaporized by the plasma as it touches.

Plates?

Plates are extremely impractical in terms of electromagnetism as plates are rather limited in the amount of length that they can add to the electromagnet. Coils make electromagnets more powerful.

So is it possible at all?

Yes, but you can't rely on the plasma providing enough current to the copper without vaporizing it. In order for it to work, you MUST have some way to prevent the copper coil from being vaporized. The only way to make sure that the coil isn't vaporized is by running enough electricity through it to create a magnetic field to repel the plasma before it gets too close.