The three worst diagrams EE students are presented with

The electric field is a vector field, it has a magnitude and a direction associated with every point in space. It's the gradient of the electrostatic potential, which could be represented by an intensity plot for all space.

arrows coming out of a dot on the center of the page ( or 8 or 24 dependin g on the book). This is what an electric field looks like on a charged part icle. Of course the new student does not know what a field is . the corre ct diagram would be a black smudge across the entire page because that migh t give some clue to the student that the field is everywhere. The notion th at the field is everywhere is not such a trivial concept and the diagram th at shows 16 arrows somehow does not really drive that point home.

-- so the answer is all sin waves. OK the whole purpose of the fourier se ries is to teach that any repetitive signal can be broken into sine compone nts and cosine components. SIN and COS ---(anybody listening?). So the fi rst problem they show the student is the case where the cos waves are mirac ulously missing. Isn't the whole point to show that you need sin and cos co mponents to faithfully make a repetitive waveform and the first thing you d o is hide the cos waves????- WTF

my experience , the perfect control loop is the slowest , most overdamped loop that you can build that is responsive enough to get the job done.

I think my prof said the exact same thing to me years ago.

How do you represent a vector field with a smudge and got no vectors?

16 arrows coming out of a dot on the center of the page ( or 8 or 24 depend ing on the book). This is what an electric field looks like on a charged pa rticle. Of course the new student does not know what a field is . the cor rect diagram would be a black smudge across the entire page because that mi ght give some clue to the student that the field is everywhere. The notion that the field is everywhere is not such a trivial concept and the diagram that shows 16 arrows somehow does not really drive that point home.

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--- so the answer is all sin waves. OK the whole purpose of the fourier series is to teach that any repetitive signal can be broken into sine compo nents and cosine components. SIN and COS ---(anybody listening?). So the first problem they show the student is the case where the cos waves are mir aculously missing. Isn't the whole point to show that you need sin and cos components to faithfully make a repetitive waveform and the first thing you do is hide the cos waves????- WTF

In my experience , the perfect control loop is the slowest , most overdampe d loop that you can build that is responsive enough to get the job done.

The point is that every point on the page needs an arrow. If you draw an a rrow on every point on the page you get a black smudge across the page. A black smudge would be just as instructive as the 16 arrows from a charged p oint.

On Saturday, October 5, 2019 at 6:22:50 PM UTC-4, snipped-for-privacy@columbus.rr.com wr ote:

rrows coming out of a dot on the center of the page ( or 8 or 24 depending on the book). This is what an electric field looks like on a charged partic le. Of course the new student does not know what a field is . the correct diagram would be a black smudge across the entire page because that might give some clue to the student that the field is everywhere. The notion that the field is everywhere is not such a trivial concept and the diagram that shows 16 arrows somehow does not really drive that point home.

IDK, worked OK for me. Kind of like the sun, or a hot body radiating. I didn't think because there were arrows that ended on a simple diagram that it meant the field just ended there instead of extending outward everywhere. It sure seems a lot better than a smudge across the whole page .

so the answer is all sin waves. OK the whole purpose of the fourier seri es is to teach that any repetitive signal can be broken into sine component s and cosine components. SIN and COS ---(anybody listening?). So the firs t problem they show the student is the case where the cos waves are miracul ously missing. Isn't the whole point to show that you need sin and cos comp onents to faithfully make a repetitive waveform and the first thing you do is hide the cos waves????- WTF

y experience , the perfect control loop is the slowest , most overdamped lo op that you can build that is responsive enough to get the job done.

Then every diagram representing any kind of fluid would be a smudge too.

If the student took any geometry they know a "ray" is represented by an arrow and it goes to infinity.

And everyone, regardless of education, knows a bunch of arrows represents motion or force that is not limited to the boundaries of the arrows but includes the space between them.

Sometimes you want something to settle to its final value, within some tolerance, in some limited time. A grossly overdamped loop is stable but slow. Critical or a bit underdamped settles clean and fast.

Your body movements are a bit underdamped for the same reason. If somebody throws a rock at your head, you want to get out of the way ASAP. If you want to catch a ball, you don't want your hand to go slow or overshoot much either.

I wouldn't want my power steering to be an overdamped loop either.

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John Larkin         Highland Technology, Inc 

lunatic fringe electronics

e 16 arrows coming out of a dot on the center of the page ( or 8 or 24 depe nding on the book). This is what an electric field looks like on a charged particle. Of course the new student does not know what a field is . the c orrect diagram would be a black smudge across the entire page because that might give some clue to the student that the field is everywhere. The notio n that the field is everywhere is not such a trivial concept and the diagra m that shows 16 arrows somehow does not really drive that point home.

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ry --- so the answer is all sin waves. OK the whole purpose of the fourie r series is to teach that any repetitive signal can be broken into sine com ponents and cosine components. SIN and COS ---(anybody listening?). So th e first problem they show the student is the case where the cos waves are m iraculously missing. Isn't the whole point to show that you need sin and co s components to faithfully make a repetitive waveform and the first thing y ou do is hide the cos waves????- WTF

In my experience , the perfect control loop is the slowest , most overdam ped loop that you can build that is responsive enough to get the job done.

arrow on every point on the page you get a black smudge across the page. A black smudge would be just as instructive as the 16 arrows from a charged point.

Wrong. The black smudge has only magnitiude. Vectors have direction and len gth, which is a distinction you can capture with arrows.

The vector field is also continuous, but representing that on a flat page w hile capturing the magnitude and direction features is a bit tricky.

The aim is to instil mathematical insight, and the arrows don't get in the way of that.

--
Bill Sloman, Sydney

arrows coming out of a dot on the center of the page ( or 8 or 24 dependin g on the book). This is what an electric field looks like on a charged part icle. Of course the new student does not know what a field is . the corre ct diagram would be a black smudge across the entire page because that migh t give some clue to the student that the field is everywhere. The notion th at the field is everywhere is not such a trivial concept and the diagram th at shows 16 arrows somehow does not really drive that point home.

Refresh my memory, a gradient is like the slope of a line, but in more dime nsions?

--

  Rick C. 

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Fire up a van de Graaff, apply glue to the globe, and toss some stiff-ish fibers at it. Wait till the glue dries before you power down.

If you can finda model with medium-length, recently washed hair...

Sorry, but a bunch of arrows indicates the movement of electrons towards areas of positive or partially-positive charge between the steps of a chemical reaction. See the issue with sweeping generalisations? ;->

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Ever heard of critical damping? There is slight overshoot..

16 arrows coming out of a dot on the center of the page ( or 8 or 24 depend ing on the book). This is what an electric field looks like on a charged pa rticle. Of course the new student does not know what a field is . the cor rect diagram would be a black smudge across the entire page because that mi ght give some clue to the student that the field is everywhere. The notion that the field is everywhere is not such a trivial concept and the diagram that shows 16 arrows somehow does not really drive that point home. n t

mensions?

Yes. Imagine a block of some substance that has varying density throughout it. At any point, the gradient is a vector that points in the direction of the fastest change in density and it's magnitude is the rate of increase.

Right, the one dimensional "gradient" is just the regular first derivative, but an operator that generates the equivalent of the "slope" when applied to a scalar function of two or more variables has to return a vector.

Like the single variable derivative on the real line itself it's a generalized operator and there are generalized formulations/tensor formulations of it so it can work in every coordinate system, can use it to map vectors to vectors too like in calculus on manifolds and "Einstein-stuff" so it's not always clear how the analogy "slope" applies in every context it's used.

Doing problems in electrostatics directly with the electric vector field representation can be annoying when you have to use calculus because the differential (like "dr", "dx" on the right hand side of an integral) is a vector, too, so making problems tractable when working directly with the vector equations in say Cartesian or polar coordinates usually involves finding an axis of symmetry such that you can treat the differentials as scalars in practice.

It's often easier to calculate the scalar potential field first and then apply the gradient to that to get the E-field of the charge configuration if that's what you need.

Drop an electron there and see where it wants to go.

--

John Larkin         Highland Technology, Inc 

lunatic fringe electronics

In free space in the absence of magnetic fields or other moving charges it's always gonna go somewhere! E = -grad(V), the divergence of E = 0 in free space, so -div(grad(V)) = del^2(V) = 0 - the Laplacian always describes the electric potential in free space. the Laplacian describes a scalar field that always takes its max or min values on the boundaries of the domain so there's no way to build some kind of "potential well" within the space to confine a charge in one spot by any arrangement of static charge distribution on the "walls"

It would sure make fusion a lot easier if you could, thanks nature u bitch :[

they can print images in textbooks in color these days!

The "heat map" shows the electrostatic potential, and then the E-field lines on top

6 arrows coming out of a dot on the center of the page ( or 8 or 24 dependi ng on the book). This is what an electric field looks like on a charged par ticle. Of course the new student does not know what a field is . the corr ect diagram would be a black smudge across the entire page because that mig ht give some clue to the student that the field is everywhere. The notion t hat the field is everywhere is not such a trivial concept and the diagram t hat shows 16 arrows somehow does not really drive that point home. m

page.

I wonder if that makes the OP happy? It's certainly way better that a smud ge.