There comes some point in teaching, where I have to introduce Coulomb's law in electricity. Here's where I always hit a dilemma: I give a series of sentences describing the properties of the Coulomb force. One sentence goes:
The force is inversely proportional to the square of the distance between them.
The issue: should I underline (or otherwise emphasize) "inversely" and "square"? Or should I underline "to" and "the"? In other words,
The force is inversely proportional to the square of the distance between them.
or
The force is inversely proportional to the square of the distance between them.
Why? Well, I always follow the properties up with various questions: for example, if a 2C charge is 10 cm from a 3C charge, the force on the 2C charge is 36 units. (I draw pictures, too.) What would the force on the 2C charge be, if the distance were 30 cm? The most common type of answer is 108 units, although 12 units comes often enough.
In other words, what I emphasize gets disregarded way too often. I'd rather that words like "the" and "of" be disregarded, rather than critical content words like "inversely" and "square".
Comments
If it were me...
I would emphasize it this way: The force is inversely proportional to the square of the distance between them.
But that's just the way I think and needed to remember it.
If it's true that most people forget the emphasized words, then go with "the", "to", etc. Because you want them to remember the rest.
I hope that helps.
Hugs,
Erin of Wis <3
No emphasis
Just put it down like you would a normal sentence. If they are taking your course then they should be smart enough to read and comprehend it without having it spoon-fed to them. If they require a crutch from you to help them learn then just maybe they aren't smart enough and shouldn't be taking the course.
I went outside once. The graphics weren' that great.
I wish...
I wish that were the case. And I wish everyone would be able to read or hear things with comprehension. The world would be a whole lot better. In fact, education wouldn't be very necessary, since there would be relatively little to actually learn.
-- Daphne Xu
What was that saying?
Goes something like this, Insanity is doing the same thing over and over and expecting a different result. I have been in situations where there was nobody to hold my hand, there were no do-overs, and no points for a good try. The standard that should be applied is there is no advancement until the current material is learned properly. If this requirement were followed perhaps the cheapening of our education will stop and having a degree or certificate will mean something.
I read a help wanted ad just the other day, a local auto supply store and engine machine shop was looking for a helper for the shop. I knew what the job entailed, basically someone to keep the floor swept, clean the equipment and grease it, that sort of thing. An entry level position where you are limited in how high you can go by your own abilities. For these they were requiring a 4yr degree! These used to be the types of jobs where a bright kid could take a 2yr course at the votech and step into a decent job with a chance for advancement. Now they want somebody with a 4yr degree. That's how worthless a higher education has become. If society is to survive and grow that has to change.
I went outside once. The graphics weren' that great.
more conversational
I think I'd say something like:
The closer together the points are, the stronger the force is between them. But it's not just a straight relationship - what Coulomb discovered when he did the math was that to get the force you had to divide by the square of the distance between those points, or as we scientists like to say, "The electric force between two particles is inversely proportional to the square of the distance between them." The equation that we know as Coulomb's Law looks like this:...
What I say
A lot of what I *say* is conversational. But writing it on the board is a different matter.
-- Daphne Xu
Just use an example
We were never told that is was Coulomb's law just the 'Inverse Square Law'.
The iron filings and a magnet would work wonders I think.
Far easier to understand the Flemings Left Hand rule (IMHO) Or was it the right hand rule?
Inverse Square
The problem I gave is the example.
The handedness: all the rules that we use (at that level) are Right-Hand-Rules (RHR). With the electric force, one has to dig rather deeply before one uses a RHR (or LHR). Torque on an electric dipole is the first example. Electromagnetic induction is the next.
A problem with iron filings and a magnet is that the Coulomb force is the electric force, not the magnetic force. Second problem is that with both magnets and iron, we're dealing with dipoles, not straight monopoles (point charges).
Coulomb's law should be the easiest to understand in electromagnetism, especially since it imitates Newton's law of gravity. Electromagnetism gets a lot harder the farther one goes.
I read a SF novel ("Eon" by Greg Bear) where they discover the source of an "inverse square" force. A couple pages later, they describe how the force got stronger as one got farther from the source. The problem isn't limited to community-college students. Another book mentioned a north-south geosynchronous orbit about the earth. A short story speculated that a sudden earth-spanning change in humanity might have been caused by a solar flare, a galactic dust storm, or a third thing that I've forgotten -- with no indication that any of those had occurred.
-- Daphne Xu
Try this...
The force is inversely proportional to the square of the distance between them.
Or maybe not.
That read better
That read better to my eyes, although maybe switching them around a bit might help?
Plus not highlighting the 'the's
So..
'The force is inversely proportional to the square of the distance between them' ?
It's a hard thing to judge honestly and these days most students seem to just google things if they get stuck anyway.
My first electronics lecturer in college used to put out 3 descriptions for each equation he showed, it helped a lot if you needed a quick refresher later on at least.
His one's would go like:
-The equation so "F ∝ D^2"
-The sentence as you wrote it.
-And a conversational rephrasing from the other side of the equation like;
'so for every meter of Distance separating them, that Distance is multiplied by itself to give you the Force value'
Nessa
How about...
How about using light as illustration? Or sound? Both follow an inverse square law, too, though sound is effected more by the medium it travels through. With light it would be easier to put things into natural language. After the inverse square law is understood, then teach it as applying to MOST sorts of point-source force. Is light a force? If it isn't, why not? How does light differ from electric force? How is it the same? You have lots of good questions for the class. :)
In general, it's better to instruct with questions than with a recital of facts. Facts are closed, questions are open.
Hugs,
Erin
= Give everyone the benefit of the doubt because certainty is a fragile thing that can be shattered by one overlooked fact.
I generally do...
I generally connect with light and gravity -- and with the surface area of a sphere. It appears that anything inverse-square is related to the surface of a sphere. (For Coulomb's law and gravity, it leads to Gauss's Law.)
-- Daphne Xu
O_O
Sticks to low level IT stuff for now but I did get the gist best with the first one.
Always been a big believer in that students (which I ended up being again) need to think about what teachers are trying to teach. And yes, use Google (one teacher's favorite phrase is 'Google is your best friend') or other ways to reference works/data. After that you could check in with the teacher to see if you got everything right.
Lynne
just over one month left before school starts again
With today's students, maybe
With today's students, maybe you should Instagram it, then make it into a game app on their phones.
Coulomb Go - capture the charged particles. Some are attracted to you, some repelled. By the inverse square of the distance. Just like the girl (ot boy) you had that crush on in high school.
Kris
{I leave a trail of Kudos as I browse the site. Be careful where you step!}
Target group?
In my opinion it all depends on the target group. Is the way of thinking new to them? In that case is there something that can be done on more common, general level?
If they have reason not to consider the subject reasonably important for them there's very little you can do in my experience.
Personally I'm an "equations person" (even though I've gone over to the dark side since). Stressing the important parts should be the most effective way. Changing it may make you lose those who do understand.
What students?
I've noticed that's mostly depends on students'level and their willingness to study (or to learn this special subject). Illustrations usually work better for experienced students and even better for repetition. For low level students I used examples like one mentioned as a task in Daphne's post, usually two or three of various types and only later questions and tasks.
I would teach
The idea that energy falls off as 1/r^2 is not just for electricity and coloumbs law.
I would teach that as a separate idea. Then promptly follow it up with coloumbs...
Dayna.
ps. I had one hell of a time understanding limits and derivatives until I saw an animation. I'm sure you can find one online for this law and the 1/r^2.
Suggest a 'hands on' demo - magnets
Pass out pairs of magnets and let students -feel- the repulsion between like poles (attraction is of course the same, but trickier to feel because of rapid 'snap-together'.
Maybe rig a 'gun': a plastic tube where first magnet is held by a pull-pin, second magnet is inserted and somehow also held. Pull release pin. If all goes well, might launch first magnet for a meter+. Tube should be only slightly larger diameter than magnets. Picture is a left to right cross section. (All the dots are because I'm lousy at HTML.)
=Caution!= Eye hazard! Physics is a dangerous sport!
... .... .... .... .... .... .... .... .... .... .... .... trigger pin
v_tube_v___________________________|_____________________
.... .... .... .... .... .... .... .... .... .... .... ._... .... ..|
. L^OADING PLUNGER Ss..nN g Nn..sS | ... .... .... .... .... .... .... .... .... .... keep clear zone
... | ... ... ... ... ... ... ... ... ... ... ... ... ^ gap as small as possible
... |______________________________________________________
... | - butt pin .... .... .... .... .... .... .... ^ tube ^
Then go on with: That force you felt, the force that launched your magnets.... (Ask class what they felt/observed) You noticed the force got much stronger as you pushed like poles closer together ...(In this setup) magnetism acts pretty much like the Coulomb force, the the Electrostatic force.
Well physicists just love equations, so here is the equation for the Electrostatic force. (Present graph of 1/distance-squared.)
...
Have fun!
PS: No, I have not built this...
PPS: The words that work, are the words that work... sigh.