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Electric and Magnetic Fields
This is a class about Sustainable Energy Systems
And we wanted to teach from the SYSTEMS perspective for strong reasons:
The first is generic:
Engineering too often looses the big picture in its attention to details
(And, as a result, engineering is often an isolated branch of a company)
A second reason is specific to the energy industry and stems from this fact:
Electrical energy cannot be efficiently stored (in large quantity)
Which implies:
After "electricity" is produced, it must be transported and used,
within milliseconds!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Preceding suggests that speed is going to be of the essence
Yes, if electricity were a simple thing, like water (to which it IS compared) . . .
Then, inability to store it would suggest the need to:
Move that "water" damned quickly from point-of-origin to point-of-use!
But "electricity" is not a simple "thing" like water, it's instead a complex mixture of:
Charge accumulation
Charge flow - In one direction ("DC") AND sloshing back and forth ("AC")
Extremely high to extremely low voltages (the analog of water pressures)
Electric AND magnetic fields
And TRANSFORMATIONS between ALL of these modes/things!
Occurring throughout the energy system, interacting at near light speed!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
This means that the energy industry is fundamentally different
Normal industries can be (and generally are are) highly compartmentalized:
Engineering & design / production / distribution / marketing / finance / . . .
Employees understand one (or perhaps two) of these areas:
Marketing person doesn't need to know about engineering and production
Product is sitting in warehouse, just got to know how to sell it!
With energy, marketeer must understand production, and even its scheduling!
And engineer must understand how / when / where product will be consumed
So classic business divisions are blurred together in energy industry!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
And everyone involved has to know a little bit about everything
Today I will start with the science that permeates the whole energy business
Specifically: What exactly ARE Electric and Magnetic Fields?
You reply: "But we got that in high school (or even junior high school)!"
You've heard about fields, but my experience suggests you're "fuzzy" about details
Such as difference between electric and magnetic fields
How/when they are created
What sort of things each can act upon (or not act upon)
How and when the fields themselves interact (or do not interact)
And then there is a really BIG question: "What exactly IS a field?"
An abstract map / mathematical artifact vs. something real and 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, in fact, 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 a slightly different versions for dealing with materials
Here, 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:
q = object's net charge
v = its relative velocity
* Microscopic equations WORK in materials, IF you account for EVERY electron and 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 do not need hyper accuracy – But DO need clear understanding!
So let's instead go back and mimic a sort of 18 -19th century discovery process:
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Our likely first close encounters with "electricity"
As seen by parents / grandparents:
http://joyerickson.wordpress.com/
2012/08/05/pull-up-something-cool/
Most likely observed with infant/toddler's freshly cleaned hair:
Because seems to require very, very fine (light) dry hair
(Suggesting that something is just barely overcoming gravity)
Or this shocking winter experience:
http://www.nachi.org/staticelectricity.htm
Both phenomena are exacerbated if you shuffle a lot
Suggesting that the act of shuffling is somehow transforming us
"Magic (carpet?) spirits" probably came into early explanations!
However, if watch REALLY closely, can occasionally see something more:
One toddler w/ wildly dancing hair
Touches second toddler w/ normal hair
=> Two toddlers both now with mildly dancing hair
Suggesting first toddler acquired SOMETHING from carpet
Which was then shared (and diluted) between the two toddlers
Enter "Pith Balls!"
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
"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 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:
Little or no
deflection!
Then remove rod
Result:
CONCLUSIONS: 1) Something IS being transferred to the first ball.
2) IT can then be shared with the second ball
3) Separated, its PARTS repel 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 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: Seem to have TWO things now!
1) These two things ATTRACT each other
As opposed to the repulsion exhibited by parts of one thing!
2) If allowed to combine, these things NEUTRALIZE / CANCEL one another
THING = "ELECTRICAL CHARGE"
TWO VARIETIES = "+" and "-" charge (so labeled because +'s cancel –'s)
"+ Charge" repels itself AND "- Charge" repels itself
BUT "+ Charge" attracts "– Charge"
(Not bad for a bit of dried out plant stem science!)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But what about the observed forces?
This WAS the same time period in which Newton was formulating his Law of Gravity
So scientists of this era would have wanted to quantify/codify involved force:
Its direction AND magnitude (and 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 above fixed base)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
From above, recording probe ball's deflection:
Here with probe ball having same charge as left fixed ball
With length of arrow denoting deflection of probe from vertical (as moved around):
+
-
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
To heck with that! MUCH easier to draw connected arrows
(As good as I could get with PowerPoint's clumsy built-in graphics):
+
-
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But I recognize this as conventional map of an electric field
+
-
Direction of Force still equals direction of arrows
But I have lost information on the STRENGTH of the Force!
Can reclaim by noticing that now have: Strength of Force a Spacing of arrows
Conclusion:
ELECTRIC FIELD => Map of FORCE on a charge (due to other charges)
ARROW DIRECTION => Direction of Force on "+ charge"
ARROW SPACING => Strength of that force
Like a topography contour map? Not quite, but can easily make the connection:
http://www.map-reading.com/ch103.php
Draw perpendiculars to topo map's contour lines:
Contour lines = Constant altitude => Constant "gravitational potential energy"
But FORCES (all forces!) a – [ GRADIENT IN ENERGY ]
That is, forces try to push things down slopes in energy
So forces are perpendicular to constant energy contour lines
Closer contours (steeper slopes) => Stronger forces
Electrical analog:
http://www.pstcc.edu/departments/
natural_behavioral_sciences/Web%20
Physics/Experim%2001.htm
Perpendicular to electric force / field lines
Are constant ("electrostatic") energy lines (a.k.a. "equipotential lines")
But a (seemingly) very important observation:
Hills do not really have embedded contour lines
Contour Maps are just artificial human way of visualizing forces & energies
Suggesting that "electric fields" are also just a visualization tool!
What is REALLY going on (which we learned in high school) . . .
Is this weird phenomenon of "force at a distance" (i.e. force w/o touching)
Where (again from high school), if we have two charges (q1 and q2):
Force on charge q1 = - q1 x q2 / [ separation ]2 ê12
where ê12 is a unit vector pointing from 1 to 2
and q's are "net charge" (amount of + minus amount of – )
(Way of dealing with more complex charge distributions: 1st Maxwell Equation)
And to be rigorous: Forceelectric = q (on object) x E (electric field at object)
(Which is just the first half of the Lorentz Force Law)
To make sure we've cleared up any remaining fuzziness:
- Electric Fields are way of mapping force (apparently* just a human abstraction)
- This is an "electric force" that can be exerted ON an object carrying a net charge
- BY another object also carrying a net charge
But adding in our knowledge that atoms arrive with equal +/- charge:
To carry a net charge 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")
Anything ELSE will remain "neutral," everywhere, ignoring electric fields
(* = to be revisited)
Pop Quiz:
You think you now totally understand charges and electric fields?
Then try to figure out what is going on here:
From the UVA Virtual Lab: "Pith Ball Ping Pong" (link to full animated presentation):
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
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 might expect a magnetic field to be a map of:
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!
Other magnet is likely to twirl all around and/or dance off to right or left!
AND / OR:
Then what IS this a map of?
Originally, probably just this – Arrangement of iron filings around a magnet:
http://www.magnetyze.com/page/magnetic-fields.aspx
Which we now sort of 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
Don't believe that 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
But do we really CARE about an iron filing map?
And why should we even dignify this pattern with the title of "magnetic field map?"
Well, 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!
Requiring a more complex set of rules to use:
In such maps:
- 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
Which would lead us to predict these forces
Parallel lines => Repulsion
Anti-parallel lines => Attraction
Or for converging/diverging lines: Torques
Parallel lines are closer together at left => Hence they repel more strongly
But for energy systems, how relevant is all of this?
We've no efficient way of moving energy via flowing magnets
But we DO have a way of moving energy via flowing charge
So let's instead try to figure out how (or even if) magnets apply force to 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!
+ -
+ -
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Magnets do not seem to affect charges!
What Magnets DO seem to affect:
- Other Magnets
- Iron
- Most Steels
What Magnets DO NOT seem to affect (contrary to popular student belief):
- Some steels (even though they are still almost entirely iron)
- Copper, brass, zinc, aluminum, gold, silver, (majority of familiar metals!)
So are magnets useless in power systems where we want to move charges?
You KNOW they are NOT useless and that they CAN affect charges
So what have we missed (and why did I add "seem" above)?
If schoolmaster Cantor had instead MOVED that magnet:
With magnet moving rapidly upward:
- Left "positive" ball would swing forward (out of page)
- 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 to vertical
If balls were discharged: Nothing would have happened
And a MOVING CHARGED BALL would be affected by a STATIONARY MAGNET
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Combining this with iron filing patterns one can (eventually) get:
The "RIGHT HAND RULE" (actually the first of TWO related Right Hand Rules):
http://www.swapyournotes.com/art
icledetail/articledetail.html/632/
PROBLEM: Early observers inferred that there are two types of charge: + & They defined "Current" as being a flow of positive charge
charge
But electrons, DISCOVERED LATER, ended up being assigned negative
Even though we also learned that THEY were the things actually flowing!
So if you work with (or try to visualize) electrons, everything gets turned around!
Can clarify via more careful / comprehensive definition of "current"
+ charges REALLY repel one another
- charges also REALLY repel one another
So from atoms on up, real matter contains ~ equal amounts of + / - charges
Which allows opposite charge attraction to ~ balance like charge repulsion
=
+
+
Now imagine that I moved the + charge to the left
First showing component charges separately, then properly overlain:
+
+
=
Now instead imagine that I moved to negative charge to the right:
+
=
+
Same result! Opposite charge moving in opposite direction = Same
+
=
=
+
+
+
But same movement direction with opposite charge gives opposite result
+
+
=
=
=
+
+
Suggesting a fix:
To figure out net movement and/or flow of charges:
Multiply the amount of charge (including its sign!)
X that charge's velocity (also including its sign/direction)
Making this more complete definition of current:
I = (positive charge) x (its velocity) – (negative charge) (its velocity)
Which is equivalent to (separating out magnitudes and signs) to:
I = (magnitude of + charge) x (its velocity) – (magnitude of – charge) (its velocity)
For forces, this is same as noticing cross product in Lorentz Force Law:
Right Hand Rule: 1st vector = thumb / 2nd vector = straightened fingers
But here 1st vector is not v, it's q v = current due to that charge
And 2nd vector is the magnetic field
Actually component of the 2nd vector perpendicular to the 1st
Rule tells you that their cross product force will be in a direction out of the palm
For + charge moving up, (q v) is UP
For – charge moving up , (q v) is DOWN
Leading to more explicit 1st Right Hand Rule:
OK, but still want to know what IS a "magnetic field?"
It's an iron filing pattern – But also something from which we can infer forces
But how do we deal with stationary charge but moving magnet?
Right Hand Rule is defined as "from the perspective of the magnet"
So magnet moving UP toward towards charge => "downward" charge flow
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
This WAS what I used to figure out earlier slide:
+
-
<= Forces on Charges
<= (q) (apparent charge velocity)
(+q on left vs. -q on right) multiplied by
(magnet: both charges are moving down)
<= REAL movement of magnet (UP)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
So, revising an earlier statement:
Magnets CAN affect charge, but only if magnet and/or charge is moving
Forces then inferred from field via RIGHT HAND RULE
Using charge velocity, as seen from magnet's perspective
And as long as you use MY VERSION (with "q Velocity" instead of plain "Velocity")
(which IS what Lorentz Force is trying to tell us!)
You will get right results for both positive AND negative charges
"Are we there done yet?"
(Almost!)
We've seen how: Moving magnets apply a force to charges
Or charges moving IN a magnet's 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-lawof-electromagnetic-induction/
Which is again reversed for negative charges
Which, 99.9% of the time ARE what actually makes up the current!
But you can sort out both RIGHT HAND RULES by either:
1) Thinking of THUMB's direction as representing = q v
= (charge with sign) x (velocity with sign)
= Current due to that charge
OR
2) Thinking of THUMB's direction = actual direction of charge movement
But then use RIGHT HAND RULE for positive charge
And equivalent LEFT HAND RULE for negative charge
Which has a nice ring of equality to me as a left-handed person!
Going back to recap first half of lecture, on Electric Fields:
Electric Fields are way of mapping Electric Force
Electric force can be exerted only ON an object carrying a net charge
BY another object also carrying a net charge
Point charge (at 2) generates an electric field E (at 1) = q / |x1 – x2|2
ê12
1st Maxwell Equation computes E field for more complex charge distributions
Force due to Electric Field = q E = (net charge on object) (Electric Field at object)
This is the first half of the Lorentz Force Law
To ACQUIRE a net charge (in even a microscopic region) a material MUST either:
Allow some charge to move in or out of it (i.e. be an "electrical conductor") OR:
Allow its charges to shift in different directions (i.e. be "polarizable" / "dielectric")
Recapping second half of lecture, on Magnetic Fields
Magnets (and their fields) act on other magnets, and iron, but not much else
UNLESS that something else has MOVING CHARGE
OR IF magnetic field is moving with respect to charges
Unlike Electric Fields, Magnetic field maps are NOT simple force maps
But they can be used to infer the forces between magnets
Can also be used to infer the force of fixed magnetic fields upon moving charges
Or force of moving magnetic fields upon fixed charges
To figure out force on moving current, apply 1st Right Hand Rule
With thumb representing direction of (q Velocity) instead of simple (Velocity)
To figure out magnetic field created BY current, apply 2nd Right Hand Rule
Again with thumb representing direction of (q Velocity) instead of simple (Velocity)
That is really ~ all the electrical science we need to know
The trick is just to figure out all of the sneaky ways it can/must be applied:
- In electrical devices (especially electricity generators and users)
- In the electrical transport system itself (a.k.a. "The Grid")
These will be subject of my next two lectures
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
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 (2014)
(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