whether we talk about forces or e fields---we are dealing...

Whether we talk about Forces or E fields---we are

dealing with vectors.

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When we dealt with Vectors in PHYSICS I ---I loved it--but still we came up with an easier way, an Energy way

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The Charge distribution--this is a picture○

The electric field map-picture○

Electric Potential---this is the new picture○

There are three different pictures that can describe what is happening with electric….everything.

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•Electric Potential and Electric Potential Energy (not the

same things)

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•Let's review gravitational potential energy and see if we can use it to help describe electric potential energy.

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CONSIDER A UNIFORM GRAVITATIONAL FIELD.

A New Hope---

Work Done By Earth Wearth=m g (d) cos()

Here Cos() is 1 since --both the force (mg) and displacement vector (d) are pointing the same way.

PEgrav= - m g d (1) The minus sign is important, it is

what happens when objects fall to lower energy, or a test mass

(positive) moves in the direction of field lines.

Let a mass mo fall from yi to yf

The Earth does work and the

gravitational potential energy decreases as the mass falls ---

downhill, to lower energy.

Notes 3 Electric Potential

Work is done by the field on a charge as it moves

As charge moves "downhill" to the potential energy decreases

The role of test mass is changed to test charge qo

Instead of g, we have E (electric field)

And displacement is still "d" and makes some direction

with field.

The same thing happens with E field.

Simple case--Uniform field.

We need to put the minus sign in for Electric Potential Energy to indicated the decrease in energy when positive test charges move along field lines.

Work Done by E field as charge is allowed to "fall" to lower energy

WE=FE*d*(cos(0))

Signs---Signs---Everywhere a sign---OK. Just look at picture. If you have

positive charge moving along field lines, that is "downhill"--lower energy.

Units are still Joules (N m) ---THE QUANTITY ABOVE IS THE CHANGE IN ELECTRIC POTENTIAL ENERGY . Many physics problems are easier to do with energy.


ELECTRIC POTENTIAL -----IS NOT THE SAME AS

ELECTRIC POTENTIAL ENERGY (CLOSE--BUT NOT)

We get to define Electric Potential difference

Electric Potential Difference=

Electric Potential ENERGY difference/charge

V=PE/qo

On the right hand side we have Joules/Coulomb or J/C. We are going to give this a name:

1 Volt=1Joule/Coulomb

Volts are used everywhere--phone or computer battery, outlet, car batteries, usb port, etc.

A slang term for ELECTRIC POTENTIAL DIFFERENCE (V) IS VOLTAGE

(DIFFERENCE).

Strange Colbert Questions now:You are a small but well liked rodent (think Stuart Little). You are

tasked with moving a 1.00kg brick to the top of a 150.0m tall building. Would you rather do this on Earth or on the Moon? I may have you lift

more bricks later.

Work per kg on Earth= g*hWork per kg on moon=gmoonh

There is less change in energy for the task done on the moon since

Gravitational field strength is less there. I don't need to know about the mass.


What does electric potential difference mean?

It is how many Joules per Coulomb of work can be done by

the charge moving say from the positive to negative terminal of a battery.

As charge moves by some electrical device it may have a high electric potential. After it has moved through some electrical device (a light or motor) the charge has less electric potential ("""" Voltage""""").

How much charge can move --we'll tackle later.

We want to apply our new tool (Electric Potential ) to our special cases of a Uniform Field and also a Point charge ---these are two separate special cases.

We have assumed that the test charge moves along the direction of the field lines, which means the charge is moving "down" the electric

potential--to LOWER ELECTRIC POTENTIAL.


Relating Units for E and V

These two different looking units are the same. This is very

important---

You will be asked about measuring Electric fields with a voltmeter and a ruler---which set of units will you use?

A problem. Take 2 parallel plates separated by 1.00cm. Hook plates to the

terminals of a 12.0Volt battery to make a field. Place an electron in the middle. Determine the speed with which the electron strikes the plate.


What is the loss in potential energy of the electron as it

moves from center to plate?

The lost PE gets converted to KE.

This is fast (do we have a limit on how fast)--and this was only 6 Volts.Imagine what can be done with thousands of Volts like in say an old CRT---monitor or old Picture tube TV (what does CRT mean).

Several Simulations to look athttps://www.compadre.org/Physlets/electromagnetism/illustration25_1.cfm

https://www.compadre.org/Physlets/electromagnetism/prob25_1.cfm

https://www.compadre.org/Physlets/electromagnetism/ex26_2.cfm--caps

https://ophysics.com/em9.html--hill


https://www.compadre.org/Physlets/electromagnetism/illustration25_1.cfm

https://www.compadre.org/Physlets/electromagnetism/prob25_1.cfm

https://www.compadre.org/Physlets/electromagnetism/ex26_2.cfm

https://ophysics.com/em9.html

The Electric Potential around a point charge

Point Charge Review:

For a point charge we saw that Coulomb's law gave the force between a source and test charge like

It takes work for me to push a test charge qo inward closer to the source charge. Like always I can display this as area under a force x displacement graph

We don't have the math to do this kind of adding. So I'll give you the answer for the potential energy ---then we will move onto electric potential.


Back to our definition of Electric Potential Difference

V=PE/qo

I could ask you to place your initial charge "far far away" or start at "infinity" …..and……come on you know it---BEYOND.If we make ri infinity--then that second term becomes zero.

Then I am going to call electric potentialV=kqs/r

The electric potential due to a source charge is given by this, when a distance "r" from the charge. I just need to take a red wire from

my voltmeter and plop it down at "r" ---and measure the difference between that electric potential and the black wire which

I connect to ???

Yes connect the black wire to infinity--otherwise known as Ground. Do you have ground wires at home?

So instead of a flat potential (sledding hill) hill like we had for the uniform field, now we have a different shaped electric potential hill.

I can think of "pushing" the

test charge up this hill to some final "height" as it

comes in from infinity.


Adding vectors sucks---for E fields•Energy is a scalar•Now I can deal with multiple charges or source distributions by just normal adding

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All the hard math was pre-done.•

Why did we do all this electric potential stuff again?

So how do I find the electric potential at the point "p"?

I add three thingsV1(at p)+V2(at p)+V3(at p)

The only geometry is to find r1 r2 r3

OK--I can't wait to try this with some numbers.

the origin 2) y=-0.05m on the y axis 1)

Place charge a, of 0.1µC, charge b of 0.1µC at + and - 0.1m along the y axis. Then find the electric potential at


Aside--Another unit of Energy: Electron Volts

If I take an electron in a uniform electric field, and drop it through an

electric potential change of 1 Volt, the electron picks up kinetic energy (loses potential energy).

This package of energy (eV) is really convenient for say bond energies. The ionization energy of the electron in hydrogen is 13.6 eV, The ionization energy for an outer electron in sodium is approx 2eV---much more convenient than Joules---

A photon of yellow light "flash" ---about 2eV.

How much light energy needs to go in, to break certain chemical

bonds?

Why do say --- x-rays break bonds in many organic materials

(thousands of electron volts ----- eV). x-rays break bonds.

Guess how to make x-rays----drop an electron through a ten thousand volt electric potential, and smash it into a piece of metal.


Conductors---(not Ringo Starr, or George Carlin or Thomas

the Train)----ELECTRICAL CONDUCTOR

What is the Electric field inside a conductor?--let's charge

the conductor

In metals it is the electrons that move, but protons (positive charges are left behind) when electrons are removed.

INSIDE THE CONDUCTOR, when I hook a wire up to a battery to add/remove charge-- the electrons keep moving (redistributing) until they stop.

The charge on a conductor "wants to spread out"--after all like charges repel. Charge IN A CONDUCTOR keeps moving until it stops. That means the charge is in equilibrium, so the net electric force on the charge is zero. There are many (like 1025 or so proton/electron pairs) with charge that might move in the material. THE E FIELD INSIDE THE CONDUCTOR IS ZERO. The charges (free to move) keep moving until E inside conductor is zero.

How about E outside? ---Good question.I can't find E everywhere, but let's get real close to the surface and look. ZOOM IN TO A PATCH.


A PATCH OF CONDUCTOR SURFACE

The patch looks like a plate---not the

whole story. Plates have E field pointing away, and we had

expression.

But the rest of charges everywhere else on conductor must add to cancel the field inside, and double it outside.

Right near the surface of a conductor--where it looks flat--the field is given by

This is just like, when near the surface of the Earth the gravitational field looks uniform.

How about pointy or sharp edges or corners of conductors? When a

metal is charged, or an E field is applied somehow, charges bunch up at corners or points. That makes the E field or Potential really big in those

regions.

Fork in microwave oven vs spoon

Mug with metal trim (burns at the edge of trim)

Lightning rod


Equipotential Lines/Surfaces---topographical maps ---

relation to E field picture and charge distribution. 1) plates, 2) point charge

The charge distribution•The E field•The "equipotentials"•

Plates1)

Three different pictures give equivalent information:

Given this charge distribution I

can draw the E field, and I can draw equipotentials (lines of

constant "voltage"). High voltage is near +, Low is near -

Given this picture (E field) (I've just

drawn between plates--not fringing at edge or zero outside)---we know that +

charges are at left, - at right. We also know that the field lines point

"down" to lower electric potential. The lines of "equi-potential" are perpendicular to field lines .Equipotential means move, but in a

direction that does not go up or down the energy hill

The Equipotential picture (topo-map)

tells us which way is downhill and how steep--that is---we can infer the "field

line map" from the equipotential map.

Any of the three pictures give equivalent

information!!!!!!


OK-what do the three pictures look like for a simple point

charge distribution.

I'm going to draw all three pictures "on one picture".

This is a good time to look at field and potential pictures in text, or physlets. Dipoles, or capacitor plates.


A capacitor is an electrical device used to store electrical energy.•The charging or release is often used to control timing•A simple model is a "parallel plate" capacitor--though many geometries can work.

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A capacitor is charged by hooking a battery up to the plates•We already know the E field between plates •

Capacitors:

Symbol Cap. Battery symbol

Ground symbol

We can think of the battery as moving

charge Q from the negative plate to the positive. Note the total charge is zero---

but we refer to the capacitor as "Charged to Q" or "Charged to the battery potential

Vbat".

During charging, the battery does WORK to

store energy on the capacitor. It takes energy to separate charge (think about it).

How does that battery do its thing--that is a chemistry question.

What is the definition of capacitance C----(don't confuse coulomb's of charge with capacitance--context matters).


Capacitance:

The definition was given as charge per volt.

Units for capacitance

1.000Farad=1.00 Coulomb/1.00 Volt

A "Farad" (after Michael Faraday) is

a large capacitance.

Big capacitance means it is easy to hold a large charge separation Q with small Electric Potential Difference.

So to find the capacitance of some electrical black box--do I just need to measure the charge Q going in the positive side when I hook a battery up? YES. However, I'd like some theory to help me design a particular capacitor.

Special Case Design theory for parallel plate capacitor

Note the capacitance does not depend on how much charge there is

(well--OK as long as not overloading and blowing up the capacitor). Q cancelled out. Capacitance depends on geometry (and the constant).


Can I combine several capacitors in a single circuit?

parallel 2) series1)

Parallel circuit elements means---the two elements (or more) are connected both across the same electric potential difference.

Note both tops of cap are

connected directly by wire to battery +, both

bottoms of caps are connected to - terminal of battery.

Can I measure the

capacitance of the dashed line black box?--yes--I know

what is in the box. Two capacitors in parallel.

When capacitors are placed in parallel, the capacitances simply add.


Capacitors in Series:

Series means that the two elements are lined up in a row in a circuit.In this case the charge into each is the same, but the voltages (electric potential drops in the circuit) must add up to the "uphills".

For potential, you may think of a roller coaster (or energy conservation). The uphill (energy gain ) from the battery--must equal the sum of all the downhills (energy losses).

OK-let's apply the definition of capacitance (upside down --since I

know the algebra works easier that way).


Practice: Given three capacitors as drawn, find the effective

capacitance of the circuit. C1=10µF C2=20µF C3=30µF

ENERGY--HOW MUCH ENERGY IS STORED IN CAPACITOR?http://physics.bu.edu/~duffy/semester2/c07_capacitor_energy.html

Moving charge q1 takes very little work since the E field is still small

The next charge may take about twice as much work, since E is

bigger

The next takes more work.

2nd some work to lift onto first

3rd lifts onto 1and 2

4 lifts higher, and so on.

HOW MUCH TOTAL

This is like lifting bricks to build a stack--first --no work

As a capacitor is charged, little by little---we move charge from one

plate to the other to charge it. q1, q2, q3, q4, q5, q6…and so on. Each charge may be equal, but we are labeling the first to move, the

next, and so on.


http://physics.bu.edu/~duffy/semester2/c07_capacitor_energy.html

Energy Cap

The energy it takes to build thatstack of bricks is the same as lifting the total mass M=n*m, halfway---so to a height of h/2.

The same with pushing charges from one plate to another on a capacitor.

Energy to charge=

For the capacitor we are building the charge distribution.This is different than we had previously with moving a test charge within an existing field, potential hill.

The difference is like saying let's lift one brick to the top of a hillor--let's build the hill with a bunch of bricks. When building the hill,

some start at the bottom.


whether we talk about forces or e fields---we are dealing...

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