Electric Fields---A new hope A review of Gravity Discussionspots.augusta.edu/tcolbert/phys1112/SU2020/Module 2...Bring in the Independence Day ship (really ff-ing big), bring in the

Electric Fields--- A new hope

A review of Gravity DiscussionWhen we learned about gravitational force, we were also learning how to deal with "forces". We kept things simple. We took typical cases like "what is the gravitational field strength if I remain here on the surface of the Earth". And we knew the answer (empirically by measuring) is g=9.8N/kg. ---Think about the units--and as always the direction is toward the center of the Earth. But what happens if we have several objects pulling on us at once gravitationally.

Bring in the Independence Day ship (really ff-ing big), bring in the moon real close, or a min/micro black hole.

It is difficult to do this with moving planets and such. But with electricity and electric charges--WE NEED TO BE ABLE TO CONSIDER MORE COMPLICATED DISTRIBUTIONS. WE NEED A NEW TOOL "ELECTRIC FIELD" TO MAKE THINGS EASIER (FOR HARD SITUATIONS).

"g" is measured in N/kg.

In our special case the Earth makes the gravitational field----but the

thing on the bottom (test mass) is the same type of thing--a "maker of gravitational field--just small

The units used to be thought of as m/s2 --but here, with hand

holding up test mass there is no acceleration---THERE IS CERTAINLY FORCE (TRY IT WITH YOU’RE A&P BOOK).

When we draw a "FIELD MAP PICTURE" We are asking---what if I

put my test mass here, and here, and here, (everywhere)….the map gives us the results everywhere we make the picture.

FIELD MAP PICTURE-gives a "how strong and which way is the

field" IF I PUT MY TEST MASS THERE AND MEASURED.

Note that "g" is the gravitational field strength

Notes 2 E field Page 1

Electric Field Definition

E=F/qtest

This is a prescription for how to measure Electric field AT A POINT IN SPACE (we may need to consider many locations).

We grab a test charge qo and measure the Net ELECTRIC force on that test charge. We are not asking yet--what makes the field (other charges). We just want to know how to measure the field with a test charge.

In General--think of that test charge as small and positive. We get to ask--what would the force be on a small positive test charge if I plopped it down right here. pictures now.


But--How do we make Electric fields? With Other electric

charges. Let's call those the "source" charges.

Consider more field pictures:

OK--so I took my tiny test

charge and moved it from A, B, C, D---and we can give a guess as to the direction of force.A---OutwardB--Outward (different direction than A)C--outward strong (lines are close together)D--outward like C--but

weaker….E field lines are far apart compared to

location C.

What do you think belongs in the MIDDLE OF THIS PICTURE? What makes this Field picture?Are the source charges positive or negative and where might they

be located?

A different picture (geometric setup) of SOURCE CHARGES makes a

different Electric Field map picture. We can makealmost any field picture.


Instead of talking about Electric forces (on a charge

someplace) we will talk about Electric Field at a location (Force divided by test charge if we so chose to put it

someplace).

It would be great to have a theory to use to tell us that if we plopped down source charges in this geometry, then we get this E field picture.

We have that: COULOMB'S LAW. But we need to modify

for E fields (so we will have a Coulomb's law for forces, for E fields, and for something later--electric potential)

so-let's look at two charges --a source charge, and a test charge (similar for gravity to "the Earth" and "me")

The field map is just a rough picture, like graph paper--there is meaning "between" the lines, and I need the entire picture to tell what is happening.

From this picture I can tell which way the source charge (or the field) exerts a force on the test charge--and how much force.

For a point positive source, the E field points away, and the strength is given by Coulomb's law. Let's check what Coulomb's law tells us.


We know a special case for Electric Forces ---between 2

point charges. This is given by Coulomb's law. So let's look at that.

But let's call charge 2 the test charge and charge 1 the source charge,

and then use our definition of E

Coulomb's law has given us an expression for answering the SPECIAL

CASE QUESTION---What is the electric field due to a point charge?

This is kind of--a new form of Coulomb's law---but for E field. If we wanted to know the E field due to a more complicated distribution of charges, then we need to Add (vector adding). We need to add vectors

everywhere---THIS CAN BE DONE, BUT REQUIRES MORE MATH. So, we will just give a few pieces of other results and pictures.


Other special Case E field pictures and or expressions.

A line of charge•A Plate of Charge•Two charges (same or opposite--dipoles•

Some Geometries:

Before doing math--Look at some simulations/pictures

https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html

You can "Plop" down positive and/or negative charges, view an arrow field (not the same as field map picture), or measure field strength using the sensor. DO IT.

When asking "what is the E field around a + point charge" we can think of the entire E field map (the whole picture), or we can ask "What is the E field at this particular point in space some distance from the source charge?". These are very different questions.

IF THEN

IF I know the E field vector at a point, and IF I know the test charge

then I can determine the force on the test charge.


https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html

Given a 10.0nC charge located at the origin, what is the

Electric field vector (magnitude and direction) at a position of 1.00m along the + y axis.

OK--now what is the E field (magnitude and direction ) at a position of x=1.00m, y=2.00m (1,2).

We could use Coulomb's law for E field special case point charge (kq/r2) to find E field strength, and then geometry to find E field ---at any location in space.

What if we have two charges? Then ADD VECTORSNO BIG DEAL


tcolbert

Pencil

Then ADD VECTORSNO BIG DEAL


They point inwardWhat is different about fields due to negative charges?

Well, if charge "A" means 4 lines, then twice the charge means 8 lines. It is our choice how to draw the scale in any given problem (just like using graph paper).

What if I have more charge?

To measure density, I need the entire picture.More "density of field lines" means a stronger field

The direction give the direction of force on a "would be, what if,

test charge".

What do those ---field lines mean?

No--NO_NO_NO_NO---"nein nein nein nein". It is not possible

to answer the question, "which way is the force on the test charge" and point in multiple directions. Physics gives one

answer to a situation

Can field lines cross?


Consider the E field due to two charges

We might ask "What is the Electric field vector at point 1, then again at 2, 3,4,5,6….everywhere.

We know that to find E(at point 1) we need to add vectors.

What does the picture look like after we do the adding?

Field due to an Electric Dipole. Is this important? WATER IS A POLAR MOLECURE (BIG ELECTRIC DIPOLE MOMENT).


Aside:---Just how big is the electric dipole-ness of water

molecules? That is called the dipole moment. We can estimate from typical bond lengths and charge. Dipole

moment refers to how much charge moves from one side of the molecule to the other, and how far. So we just need to approximate the charge and bond length

Let's say that the electron prefers one side of the molecule over the other about 1/10 th of the time---so 1/10th of an electron has moved a bond length. A typical bond length is about 0.100nm.

This is not far off of typical dipole moments for simple molecules like water.

Take a look at physlet simulation for dipole picture and trajectory

https://www.compadre.org/Physlets/electromagnetism/ex23_2.cfm

https://www.compadre.org/Physlets/electromagnetism/illustration23_3.cfm


https://www.compadre.org/Physlets/electromagnetism/ex23_2.cfm



Let's make one. Remember that you can use some of

the simulations too

What if we have a wonky E field map--picture?

On this picture, where is the E field strongest (I can kinda think of

that as steepest downhill)? And which way is the E field. I've circled the regions where E is strong--where the lines are close together.


Lines, Planes and Spheres---OH MY (--know my movie

pun/reference).

E (Point)=kq/r2 ○

For this source geometry the field drops as 1/r2 (for gravity too, light from a lightbulb, sound from a speaker--all 1/r2)-----or r-2

○

Point Charges make a field given by Coulomb's law for E fields.

Points and spheres look the same from far away.

•

The field drops off as 1/r○

This is the same as r-1○

The amount of charge per length tells me how big the

charge (density) is.

○

For a LINE of charges•

WAIT--YOU ARE FOOLING ME--THAT IS CONSTANT---DO YOU REALLY MEAN THAT THE FIELD DOES NOT DROP OFF AS I GET FURTHER AWAY FROM A FLAT PLATE OF CHARGE?

YES--

The field drops off as r-0○

Lets try it with Gravity---Step up on a chair, table, or

second floor of your house. Did "g" change. Roughly what shape does the Earth look like from your point of

view (FLAT).

○

The field of the Earth is uniform (nearly) as long as the Earth looks flattish (stay close to the Earth).

○

Let's examine this flat plate field more. ○

Is a sheet of cheap paper the same as the paper you send

your Resume on for a job application? No---the difference is the "weight"--really the density, the number of grams

per square cm.

○

For Flat plates we need the number of Coulomb's per surface area (area charge density).

○

For a PLATE of Charges•


SPECIAL CASE: A SINGLE PLATE OF CHARGE:

If I put down a positive test charge, it

tends to get pushed away. If I put more charges on plate---the push is

bigger.

We are asking about the force on the test charge at its location. The

field is created by the source distribution. The plate.

Even though a charged balloon is not flat, we can estimate the charge

and radius, and surface area, and get a charge density on the surface of the balloon.


One Plate E field

We have a number for area charge density, but what field does that give us?

This new constant relates to the electrostatic or Coulomb's constant k,

so why do we have both? Sometimes experiments are done in physics and we only learn they are related a hundred years later.

What if we have two oppositely charged plates?

In region I---the blue lines head to right, and red lines to left--these cancel. THE NET FIELD IS ZERO…in region one outside the plates.

I)

In region II----the blue lines head right, the red lines head right, the field is double that for a single plate (if both plates are charged the

same). E=/o -SPECIAL CASE FOR TWO PLATES. THIS IS A REALLY IMPORTANT SPECIAL CASE

II)

In region III---the blue lines head left, the red lines head right---and cancel. The net field is zero in region three outside the plates.

III)


E field is made by charges•I can use theory (Coulomb's law and adding) to predict E field at any given point (and again, again, again with math--to get E everywhere).

•

I can use a test charge to do the experiment and measure E at some location.

•

Point Charge (or sphere)○

Line Charge○

One plate

Two plate (red plate blue plate)

Plate of charge○

Two point charges--dipole○

I have special case E fields •

Brief Summary:


Documents

Electric Fields---A new hope A review of Gravity Discussionspots.augusta.edu/tcolbert/phys1112/SU2020/Module 2...Bring in the Independence Day ship (really ff-ing big), bring in the