Physics of magnets, actually a good question.

[Hulk]

Someone who is banned recently asked about the physics of magnets, it's actually a good question. As a high school physics teacher, here's how I explain it to my students.

Each atom of the magnetic substance creates a "domain" that acts like a tiny bar magnet, it has a north end and a south end. Magnetic field lines are thought to be emerging from the North end and entering the South end.

Fact: The north end of a magnet will attract the south end of another magnet. We don't know why, it just is that way in the same way an electron attracts a proton. The first is called magnetic force, the second electric force. We have equations to predict the intensity of the force but we still don't know why it happens. It's like gravity, sure it's caused by mass, but we don't know exactly what property of the mass creates the attraction, if we did we could make a 1kg object have the attraction of a 100 kg object, or of a 0 kg object. As Feynman said, "just because you name something, don't believe you know what it is." Or something to that effect.

Although the creation of the magnetic poles in these tiny domains is a quantum effect, it can be likened to electrons orbiting the nucleus of the atom and creating tiny currents loops. Moving charges (currents) produce magnetic fields. Although this model provides a comforable model, remember this is really a quantum effect.

In a normal unmagnetic substance, like iron, the magnetic vectors of these domains is randomly arranged so that the net effect for the substance is zero magnetic field. But for a magnetic substance the domains are all aligned in the same direction so there is a net magnetic field produced by the substance.

This permanentely magnetized substance can induce a magnetic field (poles) in another metallic substance (not all metals, they must have specific paired and unpaired electrons, again quantum physics). Basically the magnetic substance temporarily aligns the domains of the unmagnetized substance to create a magnetic field. That is why a magnet will always stick to a refrigerator, never repel like two magnets can if placed N-N or S-S.

The temp magnet will have some residual magnetic abilities until the domains randomize again. Heat will speed up this randomization since it will increase atomic motion. Heat will lessen the strength of a permanent magnet. In the same way, a magnet can be strengthened by using an electromagnet in the correct orientation.

Please forgive the sloppy explanation and the casual mixing of classical and quantum theories.

BTW, the reason a magnet works through a wood surface is because the magnetic field lines penetrate the wood and induce a field in the object above it.

A flat metal will "splay" the field lines out perpendicular to the surface and not allow much mag field to reach through the surface. So, magnetic field lines are not really stopped, only redirected.

 

[Ameesh]

my highschool physics teacher said: physics without calculus is like sex without a girl.

 

[Spendthrift]

nice, id agree with that

 

[Rallispec]

Fact: The north end of a magnet will attract the south end of another magnet. We don't know why, it just is that way in the same way an electron attracts a proton. The first is called magnetic force, the second electric force. We have equations to predict the intensity of the force but we still don't know why it happens. It's like gravity, sure it's caused by mass, but we don't know exactly what property of the mass creates the attraction, if we did we could make a 1kg object have the attraction of a 100 kg object, or of a 0 kg object. As Feynman said, "just because you name something, don't believe you know what it is." Or something to that effect.

well i'll be damned. i never knew that.

there went all my faith in the science community. Jesus, here i come.

 

[Ameesh]

Originally posted by: Spendthrift
nice, id agree with that

my highschool teacher or hulk-a-mania?

 

[Hulk]

Actually, you don't need a lot of Calculus to digest the important conceptual parts of physics. In fact, I would say that a good understanding of partial differential equations is more important than just working with integrals. Any real-life event will end up being represented as a partial differential equation. Aerodynamics (Prandle's lifting line theory), fluid mechanics (Naviar-Stokes equations), Vibrations (mass-spring-damper, okay that's an ordinary differential equation). Still, my point is that high school students don't really get into differential equations.

Calculus really lets you work with nonlinear functions when doing physics, the concepts are still the same, the "generality" of the problems is just reduced. It really doesn't do any good to bog down the majority of physics classes with tedious problems. If you can calculate the magnetic flux of a regular shaped object without calculus, or apply Gauss' law of Magnetism, making the problem "more difficult" by adding another layer of abstraction by using more complicated shapes that require Calculus will shift the onus of the problem from physics to math. Not something I want to do for a general physics class. AP physics, yes, but not first year physics students, I wouldn't be doing anyone a favor.

Granted, there are some things that are much better represented in the actual form, such as Newton's 2nd law. F=ma just doesn't cut it, F=m d^2x/dt^2 really is how that should be taught. Unfortunately, very few high school students have Calc their junior year when they take physics. And the ones that do often don't have a good enough grasp of it to "cross it over" to physics.

One of these years I'm going to teach Calculus and AP Physics so I can tailor both classes to one another.

 

[Calundronius]

Originally posted by: Hulk
In fact, I would say that a good understanding of partial differential equations is more important than just working with integrals.

Very true. Differential equations are really important in electrical engineering.
BTW, AP adv. physics was probably the most helpful class I took in high school, because that's basically where I learned the concepts behind integration and differentiation.

 

[joohang]

Originally posted by: Ameesh
my highschool physics teacher said: physics without calculus is like sex without a girl.

hahahaha

True that, brotha.

I still don't understand why my IB Physics was taught without calculus. I took subsidiary level so it wasn't too bad with just algebra, but it could've explained many things so much better. We eventually had to study simple differential and integral calculus in IB Math any ways, and it just took me a few hours of Coles notes to figure out the basic stuff.

 

[joohang]

Originally posted by: Calundronius

Originally posted by: Hulk
In fact, I would say that a good understanding of partial differential equations is more important than just working with integrals.

Very true. Differential equations are really important in electrical engineering.
BTW, AP adv. physics was probably the most helpful class I took in high school, because that's basically where I learned the concepts behind integration and differentiation.

Well I'd make some comments if I knew wtf differential equations really did.

<-- Had a really crappy Integral Calculus prof who explained it as "memorize these formulae before the exam" and the textbook didn't help much either. :|'

So what does it do?

BTW, will anyone recommend me some good books to study differential equations and second-year-level Calculus? I lost all my faith in Math professors but I do want to take some more Physics and Math courses. I really need some good books and study guides, though. Anyone?

 

[PsychoAndy]

Man, when I took Physics (about a week ago), it was Conceptual, not much plug and chug, due to the fact that the majority of people won't even progress into Precalc, where you still don't learn differential equations =\ So Physics with Calc isn't going to happen anytime soon, at least in my area.

 

[RossGr]

Actually, you don't need a lot of Calculus to digest the important conceptual parts of physics. In fact, I would say that a good understanding of partial differential equations is more important than just working with integrals.

While this is very true, that Diff Eqs are critial for any real understanding of Physics, I am not sure how you could gain any understanding of Diff Eqs without an understanding of integrals, so how can you seperate the importance of these conjugate processes. It would be like leaning division without knowledge of addtion.

Hulk,
Inspite of that minor issue, sounds to me like you do a good job of teaching a tough subject under limiting conditons. Your students should consider themselves lucky, keep up the good work.

 

[SagaLore]

Originally posted by: Ameesh
my highschool physics teacher said: physics without calculus is like sex without a girl.

I wonder if girls like calculus too. :Q

 

[PrinceofWands]

Unfortunately, very few high school students have Calc their junior year when they take physics.

hmmmmm, at my school physics (well, intro to physics anyway) was a senior course, not a junior. Intro to calc was senior too though, so it ends up being the same I guess.

 

[lawaris]

I think at the high school level ... all you need is a basic understanding of physics and calculus.

It is only at the higher levels that you understand the interdependence of physics and maths .

Then at the level of Group Theory and Advanced Quantum Mechanics , Condensed Matter Physics you will find that physics looks more like applied mathematics than pure physics

 

[Hayabusa Rider]

Good explanation. Only refinement I suggest ( and I admit it is a picky one ) is that groups of similarly aligned atoms form a domain, not individual ones. Maybe this is what you meant and I misread. This is why heating a magnet destroys its properties. The domains break down at a critical temperature (the Curie point) and does not reform.

 

[Hulk]

RossGR -

You are right, DE follow integral calculus. My point is that integral Calculus is not necessary at a first year conceptual level and if the students do have and understand integral Calculus they should be able to comprehend ordinary linear differential equations, more important for solving real-world physics problems. The only times I find integral Calculus necessary when explaining first year physics (remember this course should really be titled "Newton" since 80% of it is mechanics) is with kinematics and Newton's second law. I think they are the most important concepts since they were developed using integral Calculus. Or, actually, Calculus was developed for THEM! After that, any real application of physics requires DE. I guess I'm saying that getting into the whole Calc thing just isn't worth it for general physics students, believe me, it's hard enough for them to actually work with vectors and trig! If a student can make the jump to integral Calc, than he/she can probably also do DE.


Hayabusarider -

You are right, I meant to say that each atom CONTRIBUTES to the creation of a magnetic domain.



As far as the progression of math. My undergrad was Mechanical Engineering and here's the math we had to take:

Calculus I - Here you basically use integrals to find the area under a curve, also work with derivatives and hopefully understand that the deravative of a equation is the slope of the curve. Not much problem solving here, some related rates by the end of the semester, and integrating and differentiation of harder problems. This is where the basics are learned, do well here and the rest is not too hard.

Calculus II - Integrating and differentiating harder functions than Calc I but not much new theory.

Calculus III - An extension of Calc I to three dimensions, instead of finding the area under the curve, you find the volume inside a shape. Of course there is more but that is the gist of it.

Calculus IV - aka "Ordinary Differential Equations" - This is kind of hard to explain but basically you write equations using differentials, kind of like little "bits" of something that have to be added up to mean something. Solving the motion of a mass-spring-damper (shock absorber) requires this type of equation to be solved, or RLC electrical circuits as an EE commented above. There are closed form solutions to these types of equations, that means you can actually write out the solution, plug in numbers and get an answer.

Calculus V - aka "Partial Differential Equations" - This is where you begin to create equations that actually start to model real-life events, like the example I have in an earlier post, the lift and drag of an airplane wing. In partial differential equations you have "partial differentials" that use different variable that vary with respect to other different variables. This is tough to explain until you actually get there. Many of these equations are extremely complicated, non-linear, and do not have closed form solutions, they have to be numerically solved using computers and differential equation solvers such as "Runge-Kutta." With the emergence of high speed computers we've seen practical uses of these non-linear partial differential equation solving computers like our weather predictions, notice how much better weather forcasting has become over the last twenty years? The basic equations of fluid dynamics, the Navier Stokes equations are a set of 11 equations with 11 variables, some of these equations are simple and others complex, only a computer can solve them. Sometimes you'll also hear of Tensor calculus, this is where one is introduced to Tensors, kind of like a higher dimensional vector. Essential in understand the General Theory of Relativity.

At Rutgers, where I went to school we also had to take a class called "Applied Numerical Methods for Digital Computation." Basically how to write programs to solve non-linear differential equations. Not really hard since other people have already developed the solutions, we just had to program them in FORTRAN.

It's probably best for my students that I've forgotten much of what I've learned or else I'd really confuse them. You really can hang onto the higher level math unless you use it on a regular basis.

As for learning a bit about differential equations, get a college level Calculus textbook, at the end there will be a nice introduction to ordinary linear differential equations. Honestly though, this stuff doesn't make sense until you actually solve problems with it. When you are given a problem and you write the solution, and that solution is a differential equation, then you look up how to solve it, the math is really just a tool to solve the equation that the science gives you.