Electric and Magnetic Fields
This is very much a class about Sustainable Energy SYSTEMS
Because knowledge of energy technologies, alone, is simply not enough!
Put another way: Complete, viable, affordable energy systems are PUZZLES
Made up of many, many different PIECES
(Pieces that can be frustratingly ill-defined and/or still-changing!)
Image adapted from: http://determinedtosee.com/?p=1032
On the class's homepage I described it this way:
Suppose, today, the efficiency of solar cells rocketed to 100%, and the cost to zero!
Throwing open the door to carbon-free sustainable energy!
Right?
Wrong!
In the evenings you'd STILL end up shivering or sweating . . . in the dark
Because solar energy production peaks (at best) midday
But our energy consumption peaks in the evenings
And we can't yet effectively store that midday energy
And while it sounds like we easterners could just tap into western solar farms
We also can't yet effectively transmit that much energy that far
So here, a miraculous improvement in one single energy system PIECE
Requires vast complementary improvements in two other PIECES
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
This example also cites a ground rule of present-day energy systems:
When "electricity" is produced,
it must be transported and used,
within milliseconds!
This immediacy makes energy, as a product, almost unique!
Because almost all other products can be:
Designed by someone
Manufactured by someone else
Warehoused by someone else
Marketed by someone else
Delivered by someone else
In a process spanning months and even years!
But for energy:
Months or years => Milliseconds
Myriad loosely coupled steps => One tightly coupled system
To understand energy systems, you must not only ACCEPT this:
You must UNDERSTAND WHY these statements are 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, in doing so, go a long way toward empowering you
Because, with this knowledge, energy systems will make a lot more sense
And you will not only be able to better understand energy systems
You will be prepared to participate in their design
Thus today I will examine the question of:
What 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)
And then there is the really BIG question: "What exactly ARE fields?"
Abstract maps / mathematical artifacts vs. Something real & tangible?
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
Coulomb's Theorem
And on, and on, and on . . . !
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Most turned out to be only approximations or special cases
Which could be more generally captured in just 4 + 1 "true" physical laws:
Maxwell's Equations (microscopic):
Where: E = Electric Field
B = Magnetic Field
ρ & J = electrical charge & flow
The Lorentz Force Law:
q = object's net charge
v = its relative velocity
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Or slightly different versions for dealing with materials
Where all the effects of the material's charges are hidden away* in new D and H:
Maxwell's Equations (macroscopic):
Where: E = Electric Field
(and D = ε E)
B = Magnetic Field
(and H = (1/μ) B)
Material's properties => ε and μ
ρ & J = electrical charge & flow
The Lorentz Force Law (unchanged):
q = object's net charge
v = its relative velocity
* Earlier microscopic equations WORK in materials IF you account for EVERY electron & proton!
Advantage of Maxwell's Equations + Lorentz?
Together they cover essentially everything!
And they allow for quantitative numerical calculations
But they are (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
You may eventually want to learn more about these 4 + 1 equations, however . . .
For this class, we don't need hyper accuracy – But we DO need understanding!
So let's instead 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
"Pith Balls" allowed for closer observation
Pith = Very lightweight substance (e.g. dried stems of vascular plants)
That is able to accumulate whatever we've been talking about
Pith Ball Electroscope: Hang two such balls 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 separated balls, with DIFFERENT rods, rubbed on DIFFERENT things:
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 still equals 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
Conclusions:
ELECTRIC FIELD => Map of FORCE on a charge (due to other charges)
ARROW DIRECTION => Direction of Force acting on a "+ charge"
ARROW SPACING => Strength of that force
Like a topography contour map? Not quite, but we can easily make the connection:
http://www.map-reading.com/ch103.php
Contour lines = Constant altitude => Constant gravitational energy
But FORCES (all forces!) try to push things to lower energy
That is, forces try to push things down slopes in energy
Steeper the slope, stronger the push, thus:
Closer contours (steeper slopes) => Stronger forces
=> Forces are perpendicular to constant energy lines
Constant energy line to force line conversion for electric field:
Minus charge (~mountain valley) at left
Plus charge (~mountain peak) at right
Contour lines of constant energy (dashed)
=> Perpendicular lines of force (solid)
A SEEMIGLY VERY IMPORTANT OBSERVATION:
Hills do not actually have embedded contour lines!
Contour Maps are just artificial human way of visualizing energies & forces
Figure: www.uccs.edu/~rtirado/Ch23%20ISM.pdf
Suggesting that "electric fields" are ALSO just a visualization tool!
I.E., that "lines of force" (and the gaps between them) are not really real
And what IS really real is the weird phenomenon of:
Force at a Distance
That is, force between separated (non-touching) objects
As quantified by the high school equation:
Force on a charge q1 = - q1 x q2 / [ separation ]2 ê12
where ê12 is a unit vector pointing from 1 to 2
Or, for more complex charge distributions:
- Use Maxwell's 1st Equation to solve for the total electric field
- Then insert that calculated field into the Lorentz force law
Making sure we've cleared up any fuzziness about electric fields:
Electric Fields are a way of mapping a force (apparently* a human abstraction)
This electric force is exerted ON an object carrying a net charge
BY another object carrying a net charge
Where: Object's net charge = (Amount of plus charge) – (Amount of minus charge)
Finally, adding knowledge that atoms start out with equal amounts of +/- charge:
To carry net charge (and be affected by electrical forces) a material must either:
- Allow a charge (of some type) to move in or out of it
Which would make this material an "electrical conductor"
- Or allow its charges of different types to shift in different directions
Which would make this material "polarizable" / "dielectric"
(* = to be revisited)
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 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 field maps require a more complex set of rules to use:
- 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 form 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 + 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
But positive charge = protons trapped in atomic nuclei
If the atoms aren't moving (which they usually don't, much),
These positive proton charges won't do much moving either!
It's negative electrons, able to break away from atoms, that do most of the moving
How do we modify Right Hand Rule to get force on negative charge?
First way: Continue using RIGHT HAND, but reverse result for electrons:
Magnetic force on moving negative charge is INTO RIGHT HAND palm
Second way: Switch to LEFT HAND, then do all the regular things:
Magnetic force on moving negative charge is OUT OF LEFT HAND palm
(as force on positive charge was OUT OF RIGHT HAND palm)
Pictorially:
Taking into account that the hands depicted here are on a person facing us:
Right Hand Rule for positive charges:
Left Hand Rule for negative charges:
Applying this to the magnet approaching two oppositely 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 in preceding 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 is very easy to mess up!)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
"Are we there done yet?" Almost!
We've seen how: Moving magnets apply a force to charges
Or how charges moving IN a magnetic field feel a force
But there is one more weird connection between charge and magnetic fields:
Moving charges CREATE magnetic fields (The basis of electromagnets!)
"Lenz's Law" => Part of 4th Maxwell's Equation => 2nd Right Hand Rule:
http://www.electrical4u.com/lenz-law-of-electromagnetic-induction/
That "electric current" can involve both positive and negative charge flow
Current ("I") = direction of positive charge flow = opposite of negative charge flow
Huh? Matter contains both positive and negative charge:
=
+
+
Moving positive charge to the left:
+
=
+
Creates the same end result as moving negative charge to the right:
+
+
=
But I still prefer to show positive & negative versions of 2nd Rule:
2nd RULE - RIGHT HAND for positive charge flow:
+ Charge Flow
B Magnetic Field
Reverse magnetic field for negative charge flow OR instead use a left hand rule:
- Charge Flow
2nd RULE - LEFT HAND for negative charge flow:
B Magnetic Field
Apply these rules to a simple experiment:
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 I ALSO want 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 Right/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:
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
So are these the "action = reaction" forces countering gravity?
No, because are not in direction opposite to gravity, they are perpendicular
They are in OR Out of page, trying to get the charges running in circles!!
<= Force on negative (moveable) electrons
<= Force on positive (immovable) protons
So, if anything, "action = reaction" would be trying to twist the magnet
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
It's time for the 2nd Right/Left Hand Rule:
- Charge Flow
1st Rule: Falling magnet will induce counter clockwise
rotating electron flow (looking downward)
B Magnetic Field
2nd rule: THAT electron flow will generate
magnetic fields (in blue at right/left edges)
BUT NOW LOOK VERT 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
The movable electrons felt this magnetic field approaching
Which (via 1st Rule / Lorentz Force Law) drove PERPENDICULAR electron rotation
Moving electrons (via 2nd Rule / Lenz's Law) set up magnetic field loops
Which ended up being PARALLEL to magnet's approaching field lines
Setting up repulsion BETWEEN the 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 move beyond silly science demonstrations?
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 along the belt
Its electrons are going to be barraged with 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 (2015)
(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