physics 212 lecture 3, slide 1 physics 212 lecture 3 today's concepts: electric flux and field...

Physics 212 Lecture 3, Slide Physics 212 Lecture 3, Slide 11

Physics 212Physics 212Lecture 3Lecture 3

Today's Concepts:Today's Concepts:

Electric Flux and Field LinesElectric Flux and Field Lines

Gauss’s LawGauss’s Law

MusicWho is the Artist?Who is the Artist?

A)A) Professor LonghairProfessor LonghairB)B) Henry ButlerHenry ButlerC)C) David EganDavid EganD)D) Dr. JohnDr. JohnE)E) Allen ToussaintAllen Toussaint

WHY?WHY?

Mardi Gras is 4 weeks from todayMardi Gras is 4 weeks from today

Physics 212 Lecture 13Physics 212 Lecture 13


Our Comments• SmartPhysics scores will not be visible in the main gradebook for a

few weeks• You will need to understand integrals in this course!!!• Forces and Fields are Vectors• Always Draw a Picture First… What do the Forces/Fields Look Like?

PrelecturePrelecture

Infinite line of chargeInfinite line of charge

EELectureLecture

Finite line of chargeFinite line of charge(constant (constant ))

EEWorked ExampleWorked Example

Finite line of chargeFinite line of charge(non-constant (non-constant ))

EE

HomeworkHomework

Arc of chargeArc of charge(constant (constant ))

EE2 20

1ˆ ˆ4

dq dqE k r rr r

WORKS FOR ALL !!WORKS FOR ALL !!

The “1/4 shell problem” is not The “1/4 shell problem” is not special !!special !!

It’s the same as all the others!It’s the same as all the others!


Electric Field LinesElectric Field Lines

Direction & Density of Lines Direction & Density of Lines representrepresent

Direction & Magnitude ofDirection & Magnitude of EE

Point Charge:Point Charge:Direction is radialDirection is radialDensity Density 1/R 1/R22

0707


Electric Field LinesElectric Field Lines

Dipole Charge Distribution:Dipole Charge Distribution:Direction & Direction & DensityDensity

much more interesting…much more interesting…

simulationsimulation0808


Preflight 3

Checkpoint 3.1


The following three questions pertain to the electric field lines due to the two charges shown. Compare the magnitude of the two chargesA. |Q1| > |Q2| B. |Q1| = |Q2| C. |Q1| < |Q2|D. There isn’t enough information to determine the relative magnitude of the charges

“more field lines emanating from the charge 1, so must be more field lines emanating from the charge 1, so must be greater in magnitude.greater in magnitude.”


Checkpoint 3.3

1010 simulationsimulation

What do we know about the signs of the charges from looking at the picture?A. Q1 and Q2 have the same signB. Q1 and Q2 have the opposite sign C. There isn’t enough information to determine the relative signs of the charges

““The field lines leave one and go to the other..The field lines leave one and go to the other..””


Preflight 3

Checkpoint 3.5

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Compare the magnitude of the electric field at point A and B.A. |EA| > |EB| B. |EA| = |EB| C. |EA| < |EB|D. There isn’t enough information to determine the relative magnitude of the electric field at points A and B

““Since the electric field lines are denser near Since the electric field lines are denser near point B the magnitude of the electric field is point B the magnitude of the electric field is greater at point B than at point A.greater at point B than at point A.””


Point Charges

+2q

-q

What charges are inside the red circle?What charges are inside the red circle?

+Q +Q

-Q

+2Q

-Q -2Q

+Q

-Q

A B C D E

“Telling the difference between positive and negative charges while looking at field lines. Does field line density from a certain charge give information about the sign of the charge?”

1313


Which of the following field line pictures best represents the electric field from two charges that have the same sign but different magnitudes?

A B

C D



Electric Flux “Counts Field Lines”Electric Flux “Counts Field Lines”

SS

E dA

Flux through surface S

Integral of on surface S

E dA

““I still feel a little unclear about flux integrals. Can you go over some more example problems?” I still feel a little unclear about flux integrals. Can you go over some more example problems?”

1818


“The flux is directly proportional to the charge enclosed by the Gaussian surface, therefore Case 1 will have 2 times the flux of of Case 2 because it has two charges enclosed, versus 1 in Case 2. “

“The flux is the measure of field lines passing through the surface. Once calculated, it can be shown that the surface area of both cylinders are the same.”

Checkpoint 1

(A)(A)11=2=222 11==22

(B)(B)11=1/2=1/222

(C)(C)nonenone(D)(D)

TAKE s TO BE RADIUS !TAKE s TO BE RADIUS !

L/2

An infinitely long charged rod has uniform charge density and passes through a cylinder (gray). The cylinder in Case 2 has twice the radius and half the length compared with the cylinder in Case 1.

2323


Checkpoint 1

(A)(A)11=2=222 11==22

(B)(B)11=1/2=1/222

(C)(C)nonenone(D)(D)

TAKE s TO BE RADIUS !TAKE s TO BE RADIUS !

L/2

An infinitely long charged rod has uniform charge density l and passes through a cylinder (gray). The cylinder in Case 2 has twice the radius and half the length compared with the cylinder in Case 1.

Definition of Flux:Definition of Flux:

surface

AdE

E constant on barrel of cylinderE constant on barrel of cylinderE perpendicular to barrel surfaceE perpendicular to barrel surface(E parallel to dA)(E parallel to dA)

Case 1

sE

01 2

LsA )2(1 01

L

Case 2

)2(2 02 sE

sLLsA 22/))2(2(2 02

)2/(

L

RESULT: GAUSS’ LAW proportional to charge enclosed !

“The flux is the measure of field lines passing through the surface. Once calculated, it can be shown that the surface area of both cylinders are the same.”

WHAT IS WRONG WITH THIS REASONINGWHAT IS WRONG WITH THIS REASONING????

THE E FIELD AT THE BARREL SURFACE THE E FIELD AT THE BARREL SURFACE IS NOT THE SAME IN THE TWO CASES !!IS NOT THE SAME IN THE TWO CASES !!

barrelbarrel

EAAdE

2626


Direction Matters:Direction Matters:

0SS

E dA

ddAA

ddAA

ddAA ddAA

ddAAEE

EE

EE

EE

EE

EE

EEEE

EE

For a closed surface, For a closed surface, AA points outward points outward

2929


Direction Matters:Direction Matters:

0SS

E dA

ddAA

ddAA

ddAA ddAA

ddAAEE

EE

EE

EE

EE

EE

EEEE

EE

For a closed surface, For a closed surface, AA points outward points outward

3030


Trapezoid in Constant Field0 ˆE E x

Label faces:1: x = 0

2: z = +a3: x = +a4: slanted

0E

y

z

Define n = Flux through Face n

AA

BB

CC

1 < 0

1 = 0

1 > 0

AA

BB

CC

2 < 0

2 = 0

2 > 0

AA

BB

CC

3 < 0

3 = 0

3 > 0

AA

BB

CC

< 0

= 0

> 0

x1 2

34

dAdA

EE

0 AdE

3131


Trapezoid in Constant Field + Q0 ˆE E x

Label faces:1: x = 0

2: z = +a3: x = +a

Define n = Flux through Face n = Flux through Trapezoid

AA

BB

CC

1 increases

1 decreases

1 remains same

Add a charge +Q at (-a,a/2,a/2)

+Q

How does Flux change?

AA

BB

CC

increases

decreases

remains same

AA

BB

CC

3 increases

3 decreases

3 remains same

x

y

z

0E

x1 2

3

3636


Q

Gauss LawGauss Law

ddAA

ddAA

ddAA ddAA

ddAAEE

EE

EE

EE

EE

EE

EEEE

EE

o

enclosed

surfaceclosed

SQAdE

4141


Checkpoint 2.3

(A) increases

(B) decreases

(C) stays same

4343

““The flux throughout the entire The flux throughout the entire surface does not change as the surface does not change as the charge moves, for it is still in the charge moves, for it is still in the sphere. However, if it was moved sphere. However, if it was moved outside of the sphere, the fluxes outside of the sphere, the fluxes would be different because one would be different because one would be zero!would be zero!““


““charge is closer, field is larger, more charge is closer, field is larger, more lines through a so increase in flux.lines through a so increase in flux.““

““as long as the charge is within the as long as the charge is within the shell, the flux will remain the sameshell, the flux will remain the same” ”

Checkpoint 2.1

(A)dA increasesdB decreases

(B)dA decreasesdB increases

(C)dA stays samedB stays same

4444


The total flux is the same in both cases (just the total number of lines)

The flux through the right (left) hemisphere is smaller (bigger) for case 2.

11 22

Think of it this way:Think of it this way:

4545


Things to notice about Gauss’s LawThings to notice about Gauss’s Law

If If QQenclosedenclosed is the same, is the same, the flux has to the flux has to be the samebe the same, which means that the , which means that the integral must yield the same result integral must yield the same result for any surfacefor any surface..

o

enclosed

surfaceclosed

SQAdE

4747


Things to notice about Gauss’s LawThings to notice about Gauss’s Law

In cases of high symmetry it may be possible to bring In cases of high symmetry it may be possible to bring EE outside outside the integral. In these cases we can solve Gauss Law for the integral. In these cases we can solve Gauss Law for EE

So - if we can figure out So - if we can figure out QQenclosedenclosed and the area of the and the area of the surface surface AA, then we know , then we know EE ! !

This is the topic of the next lecture…This is the topic of the next lecture…

“Gausses law and what concepts are most important that we know .”

o

enclosed

surfaceclosed

QAdE

o

enclosed

surfaceclosed

QEAAdE

0

enclosedQE

A

4848


Final Thoughts….• Keep plugging away

– Prelecture 4 and Checkpoint 4 due Thursday– Homework 2 due next Tuesday … 7 questions mostly Gauss’ law –

try them today!

5050

physics 212 lecture 3, slide 1 physics 212 lecture 3 today's concepts: electric flux and field...

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