Download Electric and Magnetic Fields

Electric and Magnetic Fields
In our first meeting I argued that you MUST understand whole ENERGY SYSTEMS
And not just one or two particularly new & exciting technologies
Because (I claimed) if a piece cannot work effectively with all of other pieces
It's very likely that it will be marginalized, or not even used at all
An example? Solar PV's struggle to become even a 3-4% contributor!
Compounding this is a ground rule of present-day energy systems:
When electrical power is produced, it must be transported and used,
within milliseconds!
To understand energy systems,
you must really UNDERSTAND WHY this statement is true
So this lecture (and the next) are a bit geeky & nerdy (OK . . . more than a bit)!
But bear with me because I believe I can make some technical stuff far clearer
And with this knowledge, energy systems will make a lot more sense
Which will go a long way toward empowering you
So jumping in the deep end, today we will ask:
What exactly are Electric and Magnetic Fields?
You reply: "But we studied that in high school (or even junior high school)!"
Well you've heard about fields, but experience tells me you're "fuzzy" about details
Such as the difference between electric and magnetic fields
Or how and when they are created
Or what sort of things each act upon (or do not act upon)
Or how and when the fields themselves interact (or do not interact)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
To get started: We are after practical, easily useable knowledge
For electric and magnetic fields, such knowledge was accumulated via observation
Mostly during the 18th and 19th centuries
Observations which (at least eventually) came to be called "Laws" or "Theorems":
Ohm's Law
Faraday's Law
Lorentz Force Law
Ampere's Law
Thevenin's Theorem
Snell's Law
Joules's Law
Lenz's Law
Kirchhoff's Law
Curie's Law
Gauss's Law
Biot-Savart Law
Reciprocity Theorem
Superposition Theorem
Norton's Theorem
And on, and on, and on . . . !
Coulomb's Theorem
These turned out to be mostly approximations or special cases
Which were eventually captured in just 4 + 1 "true" physical laws, starting with:
Maxwell's Equations:
Where: E = Electric Field
B = Magnetic Field
The key things are really ρ = electrical charge (in the 1st equation)
And J = the flow of that charge (in the 4th equation)
Because from ρ & J, Maxwell's Equations allow one to figure out E & B!
But why might one want to figure out E and B?
Because electric and magnetic fields (E & B) create forces on charges
Which drive ELECTICAL MOTORS and ELECTRICAL GENERATORS
Those forces are defined in a fifth equation, the Lorentz Force Law:
Where:
q = charge on an object
and
v = charge's velocity
1st term: Electrical force is proportional to the intensity of the electric field
2nd term: Magnetic force is proportional to charge's velocity AND magnetic field
But those screwy arrows turn out to be really important!
As does that "x" which does NOT denote simple multiplication!
Which makes Maxwell's Equations + Lorentz Law very hard to use
Because they are, in fact, (wretchedly complex) vector calculus equations:
's are not quantities but 3D differential operators, and
's are 3D "cross products" mixing up (screwing up?) x, y, z components
If they are so complex and hard to use, why bother?
Because together they describe essentially everything!
AND they allow for quantitative numerical calculations
But, for this class, we only need to understand some things, qualitatively
So let's go back to the 18 -19th century discovery process:
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
A humans' first close encounters with "electricity:"
A shocking winter experience:
http://www.nachi.org/staticelectricity.htm
Or, as seen by parents / grandparents:
http://joyerickson.wordpress.com/
2012/08/05/pull-up-something-cool/
Most likely occurring when infant/toddler has freshly cleaned hair:
Because, somehow, it seems to require very, very fine (light) dry hair
Suggesting that "something" is just barely overcoming gravity!
Both phenomena are exacerbated if you shuffle a lot
Suggesting that the act of shuffling somehow transforms us
"Magic carpet spirits?"
"Ancient Aliens?" 1
However, if you watch REALLY closely, you can occasionally see something more:
One toddler starts with wildly dancing hair
He/she touches second toddler w/ normal hair
=> Two toddlers both now with mildly dancing hair
Suggesting that first toddler acquired SOMETHING from the carpet
Which was then shared (and diluted) between the two toddlers
Enter "Pith Balls!"
1) To their everlasting shame (I hope!), "Ancient Aliens" is probably a "History Channel" trademark
What are "Pith Balls?" - Examples from YouTube:
From the Kahn Academy (link):
Or from Saint Mary's University (link):
But such experiments can be really difficult , as noted by this gentleman (link):
(All three of these videos are cached on this lecture's "Resources" webpage – link)
So let me describe "Pith Ball" experiments under ideal conditions:
Pith = Very lightweight substance (e.g. dried stems of vascular plants)
That is able to accumulate whatever that "thing" is that we get from rugs
Pith Ball Electroscope = Two such balls hanging side-by-side from strings
Touch with rods that have been rubbed on cloth / fur
Observe deflection of balls from vertical hanging
As first done by British schoolmaster John Canton in 1754:
Before:
After:
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Dissecting that behavior:
Separate the balls, touch only ONE ball with rubbed rod (here labeling ball by red):
Start:
Momentarily
push balls together
(e.g. w/ glass rod):
After touching
left ball only:
Little or no
deflection!
Then remove rod
Result:
CONCLUSIONS: 1) Something was transferred to the first ball.
2) IT was then be shared with the second ball
3) Separated, its PARTS repelled one another
Repeat with very different rod / rub:
Start:
After touching
right ball:
Momentarily
push balls together
(e.g. w/ glass rod):
Then remove rod
Result:
SEEMS to be the same: Something that can be shared & repels parts of itself
But is it the SAME thing or a NEW thing that acts similarly?
To test, treat each ball differently:
Touch each separated ball, with a DIFFERENT rod, rubbed on a DIFFERENT thing:
Touch ball 1
with rod 1:
Then touch ball 2
With rod 2:
Nothing!
Attraction!
But if they actually
touch:
Then
back to nothing:
?
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Whoops: We now seem to have TWO things!
1) These two things ATTRACT each other
As opposed to the repulsion exhibited by parts of the same thing!
2) If allowed to combine, these things NEUTRALIZE / CANCEL one another
After considerable analysis and debate, "natural philosophers" concluded:
THING = "ELECTRICAL CHARGE"
TWO VARIETIES = "+" and "-" charge (so labeled because +'s cancel –'s)
"+ Charge" repels itself
AND
"- Charge" repels itself
BUT "+ Charge" attracts "– Charge"
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But what about the observed forces?
This WAS in same time period when Newton was formulating his Law of Gravity
So scientists of this era would have wanted to quantify/codify forces involved:
Both its direction AND magnitude AND its dependence on + / - charges
Likely tried some variation of: Two large and/or fixed pith balls + 1 small probe ball
Side view:
"Probe" ball (which could be charged + OR –)
?
+
?
-
Large balls: one charged +, one held (on insulators) above fixed base
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Looking from above, recording the probe ball's deflection:
Here with a probe ball having same charge as left fixed ball
Length of arrow = Amount of deflection/swing (proportional to force)
of the hanging probe ball, when it is at that position
+
-
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But it's MUCH easier to merge the arrows together:
This was as good as I could get with PowerPoint's clumsy built-in graphics:
(Toggle back an forth to preceding slide to see what I've done)
+
-
Now THIS is recognizable as the map of an electric field:
+
-
Direction of Force = Direction of arrows
But by merging arrows, I have lost information on the STRENGTH of the Force!
Can reclaim by noticing that now have: Strength of Force a Spacing of arrows
Summarizing Electric Fields and Electric Forces:
Electric Fields are a way of mapping out Electric Forces
This electric force is exerted ON an object carrying a net charge
BY another object carrying a net charge
Net charge = (Amount of plus charge) – (Amount of of minus charge)
That force is:
1) Proportional to the electric field AND
2) Proportional to the net charge on the object
Which is what 1st term of the Lorentz Force Law was trying to tell us:
Where E field can be calculated via 1st Maxwell equation (a.k.a. Gauss's Law):
Moving on to magnetic fields:
We know Magnetic Fields are "sorta like" Electric Fields
Which mapped force ON an electric charge BY another electric charge
So, by analogy, we might expect a magnetic field to be a map of:
The force on a magnet caused by another magnet
So these arrows depict force on 2nd magnet (and hence its direction of movement)?
http://spmphysics.onlinetuition.com.my/2008/06/
introduction-to-magnetism-revision.html
Wrong!
The other magnet twirls around and/or dances off to right or left
AND / OR:
(which I can demonstrate with two bar magnets I brought to class)
Then what IS this a map of?
Originally, probably just this: The arrangement of iron filings around a magnet
http://www.magnetyze.com/page/magnetic-fields.aspx
Which we "explain" by saying iron filings like to draw in "magnetic lines"
So they end up rotating to put their long axes parallel to those lines
But once rotated, filings aren't "forced" along these lines, they just sit there!
So this isn't even a map of the force field acting on iron filings!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
You don't believe that this is really all that occurs?
For instance, that once rotated into alignment, the filings just STOP moving?
Then take a look at the "3D Magnetic Field Demonstrator" I brought to class:
http://www.magnetyze.com/page/magnetic-fields.aspx
Pasco Scientific (www.pasco.com): Model SE-8603
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Why should we CARE about an iron filing map?
And why should we dignify this pattern with the title of "Magnetic Field Map?"
From above: Electric field map was tool for figuring out forces on charges
By analogy: Magnetic field map should be tool for figuring out forces on magnets
It is, sort of, but it's an indirect tool because magnetic forces are STRANGE!
And magnetic fields require a more complex set of rules such as:
- Parallel "magnetic lines" repel each other
- Anti-Parallel "magnetic lines" attract each other
- Closer the lines, stronger the effect
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Applying those rules, we'd instead predict forces like this:
Parallel lines => Repulsion
Anti-parallel lines => Attraction
(Which IS how my two bar magnets DO move!)
Or for converging/diverging lines we'd expect torques
Parallel lines are closer together at left => Hence they repel more strongly
But for energy systems, how relevant is magnet to magnet force?
Electricity consists of moving energy via flowing charge
Be we have no comparable way of moving energy via flowing magnets
So let's turn to a different question: Can magnets move charges?
What if schoolmaster Canton had brought magnet up to his charged pith balls?
Start:
Finish:
Charged up and
ready to go!
Nada!
Nichts!
Niente!
Nothing!
+ -
+ -
(I would demonstrate this but found that it just doesn't work in our humid Virginia Augusts!)
Magnets do NOT seem to affect charges!
Magnets ONLY seem to affect:
- Other Magnets
- Iron
- Some Steels
Yes! Contrary to popular student belief (!) magnets ONLY affect:
- Iron + some steels (even though steel is always ~97% plus iron)
And magnets DO NOT affect:
- Copper, brass, zinc, aluminum, gold, silver, (majority of familiar metals!)
To prove this, I've brought in a "horseshoe" magnet and random metal objects:
?
"Houston, we have a problem!"
You know that recyclers use (electro) magnets to pull metal out of garbage:
But I just showed you that magnets attract only iron and some steels!
So how DO we recycle, for instance, aluminum?
Which we DO recycle, and very efficiently: 80-90%
Because recycling takes ~ 1/20 the energy of extracting new aluminum
Photo: http://www.bbc.co.uk/schools/gcsebitesize/science/triple_aqa/keeping_things_moving/the_motor_effect/revision/2/
The answer comes from the fact that:
While stationary magnets have no effect upon charges
MOVING MAGNETS drive charges crazy!
THIS can be used to sort and recycle ALL metals
But even more importantly:
Moving magnets and charges make electric motors work
And they are also the KEY to GENERATING ELECTRICITY
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
If schoolmaster Cantor had quickly MOVED his magnet:
With magnet moving rapidly upward:
- Left "positive" ball would swing forward (out of page's plane)
- Right "negative" ball would swing backward (into page)
+
-
With magnet instead moving rapidly downward:
- Directions of all swings would be reversed
When magnet stopped: balls would swing back into plane
If balls were discharged: Nothing would have happened
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
From this + iron filing patterns they (eventually!) deduced:
The "RIGHT HAND RULE" (actually the first of TWO related Right Hand Rules):
Using the iron-filing map of the magnetic field, for each point in that map:
1) Point your four parallel fingers in the direction of the magnetic field
Figure out the direction any positive charge is moving (with respect to that field):
2) Point your thumb in the direction of that positive charge movement
THEN:
3) The FORCE on that moving positive charge is forward, out of your palm
Now that is all fine and good, HOWEVER (!):
The ONLY positive charges we typically have are protons
Which are generally locked inside the nuclei of atoms
With those atoms generally locked in place by atomic bonds
So protons just don't do much moving around!
And in fact, protons are ~ irrelevant to electrical power
Which, as the name suggests, is instead all about electrons
But Right Hand Rules were designed to describe positive charges
With physicists lamely saying: "First work things out for positive charges,
then if its a negative charge, flip all the results around"
Why not just use LEFT HAND RULES for electrons ? (Its a lot less confusing!)
Pictorially:
Right Hand Rule for positive charges:
Left Hand Rule for negative charges:
Where the "motion" is from the perspective of the magnet
(i.e., as if the magnetic field was stationary)
Now, use this to figure out what would have happened if Schoolmaster Canton
had moved a magnet toward his plus and minus charged pith balls:
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Magnet is actually the thing doing the moving:
But from preceding, for 1st Rules motion is measured from the magnet's perspective
From this moving magnet's perspective:
Both charges are moving down
+
-
Applying Right Hand Rule to the positive charge
Rotating to align thumb with motion:
Force on the positive charge is OUT of page
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Now working things out for the negative charge:
Which is also moving downward from the magnet's perspective
Applying Left Hand Rule to the negative charge:
First rotating to align thumb with movement
+
-
But to align fingers with the magnetic field
we need to rotate hand about vertical axis
(for which I don't have a graphic)
But which would flip green force arrow INTO page
Combining those Right/Left hand analyses for the + and – charges:
Force on the plus charge is OUT of page
+
-
Force on minus charge is INTO page
Phew, that was a lot of work!
And it's very easy to mess up!
(I had to correct these figures more than once!)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Summarizing Magnetic Fields and Magnetic Forces:
Magnetic Fields are a way of mapping out Magnetic Forces
But, unlike immensely easier electric fields and forces,
Magnetic fields and forces are absolutely screwy!
They are described in the 2nd term of of the Lorentz Force Law
That force is
1) Proportional to the magnetic field (B) AND
2) Proportional to charge's velocity (relative to B field) AND
3) Proportional to the net charge on the object
But direction of that force comes from either:
Using vector calculus's "x operator"
OR (equivalently), from 1st Hand Rules:
"Are we there done yet?" Almost!
We still need to know how one calculates the magnetic field
It comes out of the 4th Maxwell equation (a.k.a. Lenz's Law):
Ignore last term, and complexities of
and
vector calculus operators
Remainder says magnetic fields (B) are proportional to the charge flow: J
This is "electromagnetism!" - Remember wrapping wire around nails?
Trick is then to figure out direction of that "induced" magnetic field
Which can be done by:
1) Learning how to use those two vector operators OR
2) Coming up with a 2nd set of Hand Rules
Taking easy way: Direction of magnetic field "induced" by charge flow =
2nd Right Hand Rule for positive charge flow:
2nd Left Hand Rule for negative charge flow:
+ Charge Flow
B Magnetic Field
- Charge Flow
B Magnetic Field
Thumb in direction of + charge flow,
Magnetic field is along curled fingers
Thumb in direction of - charge flow.
Magnetic field is along curled fingers
Using ALL of this to explain a classroom experiment we CAN do:
1 Magnet
1 Metal slug
Object of experiment: Identify which one is magnet
Test results:
NEITHER seems to pay any attention to copper pipe
Slotted
clear plastic lined
copper pipe
No reason metal slug OR magnet should!
So would expect BOTH to just fall down through pipe
Do they?
Or does ONE behave VERY differently?
Apparatus from: American Scientific (american-scientific.com): AR-105
One object just floats down the pipe!
And because it acts so strangely, that one must be the magnet!
But we need to figure out WHY it seems to almost defy gravity
Partially thwarted gravitational force
Copper (conductor!):
- Containing moveable electrons
- Thru which B field is trying to MOVE downwards
(Sounds like we might be on to something!)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Time to pull out 1st Left Hand Rule:
Force on minus electrons due to movement relative to B:
- Magnet is what is really moving (down)
- But magnet sees copper's electrons moving UP
On the leading (lower) edge of the falling magnet:
Bottom Left Wall of Pipe:
Bottom Right Wall of Pipe:
Magnetic field lines point RIGHT
Magnetic field lines point LEFT
Magnet sees electrons moving up
Magnet sees electrons moving up
Force on electrons is out of page
Force on electrons is into page
Have we found our gravity-canceling force?
No, because the forces on the electrons are perpendicular to gravity, its
Our electrons end up running in circles!!
<= Force on negative (moveable) electrons
So Newton's "action = reaction" should be trying to TWIST the magnet
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Time to add effect of 2nd Left Hand Rule:
- Charge Flow
1st Rule: Falling magnet induced counter clockwise
rotating electron flow (looking downward)
B Magnetic Field
2nd rule: THAT electron flow will now generate
magnetic fields (in blue at right/left edges)
BUT NOW LOOK VERY CLOSELY:
Magnetic lines from flowing electrons
are PARALLEL to magnet's field lines
Magnet's fall squeezes these together
causing UPWARD repulsion of lines
Tending to push magnet upward
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Putting this all together:
Gravity pulled the magnet downward
Sweeping the magnetic field down through the walls of the copper pipe
Movable electrons felt this magnetic field approaching
1st Rule / Lorentz Force Law thus drove PERPENDICULAR electron rotation
Via 2nd Rule / Lenz's Law those moving electrons then set up magnetic field loops
Which ended up being PARALLEL to the magnet's approaching field lines
=> Repulsion BETWEEN magnetic lines
=> Force directed upward!
Opposing the downward gravitational pull on the magnet
PHEW! (I warned you about how "sneaky" these "simple" laws could get!)
But can we also explain important real world things?
In the next lecture I will explain HOW this allows us to build
Electric motors, electric generators . . .
= The heart of electric energy systems
But for now, let me show you how the preceding allows us to recycle ALL metals
THIS didn't work because magnets will NOT grab most metals:
But ALL METALS contain nicely moveable electrons
So at the trash recycling plant:
Embed magnets in the roller at the end of a trash conveyer belt:
As that roller rapidly rotates, magnets are whipping up toward the top of belt
Slinging their magnetic fields upward and to the left
When that block of metal approaches the end of the belt
Its electrons are going to be pummeled by those moving magnetic fields
=> Forces that will push electrons (and block) up off the belt!
So while the trash will fall off the end of the belt:
ALL metals will be slung upward
Allowing them to jump over a barrier
Onto a second conveyor now carrying away ONLY metals
Or flicking them into a separate "metals only" bin:
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Movie of actual metal picking conveyer:
From the "American Recycling Center:"
Copy of video cached on this lecture's "Supporting Materials" Webpage:
Supporting Materials: Metal Sorter
https://www.youtube.com/channel/UCurq7PjCvPBx4zZ6v0i0wGw
Credits / Acknowledgements
Some materials used in this class were developed under a National Science Foundation "Research
Initiation Grant in Engineering Education" (RIGEE).
Other materials, including the "UVA Virtual Lab" science education website, were developed under even
earlier NSF "Course, Curriculum and Laboratory Improvement" (CCLI) and "Nanoscience Undergraduate
Education" (NUE) awards.
This set of notes was authored by John C. Bean who also created all figures not explicitly credited above.
Copyright John C. Bean (2017)
(However, permission is granted for use by individual instructors in non-profit academic institutions)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm