physics 212 lecture 5, slide 1 physics 212 lecture 5 today's concept: electric potential energy...

Physics 212 Lecture 5, Slide Physics 212 Lecture 5, Slide 11

Physics 212Physics 212Lecture 5Lecture 5

Today's Concept:Today's Concept:Electric Potential EnergyElectric Potential Energy

Defined as Minus Work Done by Electric Defined as Minus Work Done by Electric FieldField

MusicWho is the Artist?Who is the Artist?

A)A) Tito PuenteTito PuenteB)B) Buena Vista Social ClubBuena Vista Social ClubC)C) Louis PrimaLouis PrimaD)D) Freddie Omar con su bandaFreddie Omar con su bandaE)E) Los Hombres CalientesLos Hombres Calientes

Cuban Jazz !!Cuban Jazz !!

Thanks to Ry Cooder for bringing these Thanks to Ry Cooder for bringing these guys to our attention !!guys to our attention !!

Why ??Why ??

Cuban Jazz at Krannert (Ellnora) Cuban Jazz at Krannert (Ellnora) Friday night (10:30pm)Friday night (10:30pm)

Marc Ribot y Cubanos PostizosMarc Ribot y Cubanos PostizosRemembering Arsenio RodriguezRemembering Arsenio Rodriguez

FREEFREEPhysics 212 Lecture 5Physics 212 Lecture 5


Your CommentsYour Comments

05

““This really seems like a rehash of mechanics with electric This really seems like a rehash of mechanics with electric charges instead of masses.” charges instead of masses.”

““Labor Day Weekend and Physics must definitely have the same charge because the Labor Day Weekend and Physics must definitely have the same charge because the weekend kept pushing the homework and this prelecture from getting done.” weekend kept pushing the homework and this prelecture from getting done.”

““Had there been office hours this week I definitely would have Had there been office hours this week I definitely would have been there. I'm still not 100% sure about Gauss' Law.”been there. I'm still not 100% sure about Gauss' Law.”

““When solving for the potential energy, does r1 get subtracted from When solving for the potential energy, does r1 get subtracted from r2? or is it the other way around?” r2? or is it the other way around?”

““Please discuss in lecture about how the point charges will affect the Please discuss in lecture about how the point charges will affect the electric field in different situations where it has both same charge or electric field in different situations where it has both same charge or where it has opposite charges. I am confused about this. Also, where it has opposite charges. I am confused about this. Also, please go over the potential energy equation to refresh my memoryplease go over the potential energy equation to refresh my memory..””

““Homework problem style examples would be helpful, the Homework problem style examples would be helpful, the checkpoints felt too easy.”checkpoints felt too easy.”““Still generally confused on some questions about the Still generally confused on some questions about the potential energy, like the third checkpoint.”potential energy, like the third checkpoint.”

Discussion Sections Discussion Sections this week should this week should

helphelpWORKED EXAMPLES!

Right! Nothing Right! Nothing really newreally new

SIGNS!SIGNS!

Example today: Example today: calculation for CP 3calculation for CP 3

http://online.physics.uiuc.edu/courses/phys212/fall11/

http://online.physics.uiuc.edu/courses/phys212/fall11/


2

1

r

r

W F drRecall from physics 211:Recall from physics 211:

TOTW K

FFdrdr W = 0W = 0 Constant speed ( Constant speed ( K = 0 K = 0 ))

FFdrdr W > 0W > 0 Object speeds up ( Object speeds up ( K > 0 K > 0 ))

W < 0W < 0 Object slows down ( Object slows down ( K < 0 K < 0 ))FFdrdr

FFdrdr

oror

9


Potential Energy

conservativeU W If gravity does negative work, potential energy increases!Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases.

++ ++FF

++ ++xx Coulomb force does negative workCoulomb force does negative work

Potential energy increasesPotential energy increases


Checkpoint 4Checkpoint 4A charge is released from rest in a region of electric field. The charge will start to moveA charge is released from rest in a region of electric field. The charge will start to move

A) in a direction that makes its potential energy increaseA) in a direction that makes its potential energy increase

B) in a direction that makes its potential energy decreaseB) in a direction that makes its potential energy decrease

C) along a path of constant potential energyC) along a path of constant potential energy

34

““Since potential energy is negative, the charge will Since potential energy is negative, the charge will try to increase its potential energy, bringing it to try to increase its potential energy, bringing it to zero..” zero..”

““It wants to go to a spot with less PE.” It wants to go to a spot with less PE.”

““constant potential energy would require no work to constant potential energy would require no work to preform.”preform.”

FF

xx

It It willwill move in the same direction as F move in the same direction as F

Work done by force is positiveWork done by force is positive

U = -Work is negativeU = -Work is negativeNature wants things to move in such a way that PE decreasesNature wants things to move in such a way that PE decreases


FFEE FFHHEE drdr

WWHH is the work done by the hand on the ball is the work done by the hand on the ballWWEE is the work done by the electric field on the ball is the work done by the electric field on the ball

Which of the following statements is true:Which of the following statements is true:

A)A) W WHH > 0> 0 and and WWEE > 0> 0 B)B) W WHH > 0> 0 and and WWEE < 0< 0C)C) W WHH < 0< 0 and and WWEE < 0< 0D)D) W WHH < 0< 0 and and WWEE > 0> 014

You hold a positively charged ball and walk due west You hold a positively charged ball and walk due west in a region that contains an electric field directed due in a region that contains an electric field directed due east.east.

Example: Charge in External FieldExample: Charge in External Field


FFEE FFHHEE drdr

B)B) W WHH > 0> 0 and and WWEE < 0< 0

Conservative force: Conservative force: U = - WU = - WEE

Not a conservative force.Not a conservative force.Does not have any Does not have any UU..

IsIs UU positive or negative?positive or negative?

A)A) PositivePositiveB)B) NegativeNegative

16


Example: Getting the signs rightExample: Getting the signs right

In In case Acase A two negative charges which are equal in magnitude are two negative charges which are equal in magnitude are separated by a distance separated by a distance dd. In . In case Bcase B the same charges are the same charges are separated by a distance separated by a distance 2d2d. Which configuration has the highest . Which configuration has the highest potential energy?potential energy?

A)A) Case ACase AB)B) Case BCase B

dd

2d2d

Case ACase A

Case BCase B

22


Example: Getting the signs rightExample: Getting the signs right• As usual, choose As usual, choose U = 0U = 0 to be at infinity: to be at infinity: 1 2

0

1( )4q qU r

r

U(r)U(r)

00 rr

ddCase ACase A

2

0

14AqU

d

U(d)U(d)

2

0

14 2BqU

d

2d2dCase BCase B

U(2d)U(2d)

UA > UB

23


Example: Two Point ChargesExample: Two Point Charges

qq11 qq22

dd

Calculate the change in potential energy for two point charges originally very far apart moved to a separation of “d”

1 22

12

d q qU k drr

1 2q qU kd

Charged particles w/ same sign have an increase in potential energy when brought closer together.

For point charges often choose r=infinity as “zero” potential energy.

19

1 2

0

14

q qd


Checkpoint 1Checkpoint 1

“It is inversely proportional to the first radius.”It is inversely proportional to the first radius.”

“Simple conservation of energy problem: final Simple conservation of energy problem: final potential minus initial potential should equal potential minus initial potential should equal change. change. ”

““1/r1 will be larger then 1/r2 and this must be 1/r1 will be larger then 1/r2 and this must be positive”positive”

34

0 1

14initial

QqUr

0 2

14final

QqUr

0 2 1

1 14f iQqU U U

r r

Note:Note: +q moves +q moves AWAYAWAY from +Q. from +Q. Its Potential energy Its Potential energy MUST DECREASEMUST DECREASEU < 0U < 0

A charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1 away from +Q. Then it is moved to a new position at a distance R away from its starting point on a straight path. The final location of +q is at a distance r2 from +Q.

What is the change in the potential energy of the charge +q in the process?A. kQq/R B. kQqR/r1

2 C. kQqR/r22

D. kQq(1/r2 - 1/r1) E. kQq(1/r1 - 1/r2)


Potential Energy of Many ChargesPotential Energy of Many ChargesTwo charges are separated by a distance d. What is the change in potential energy when a third charge q is brought from far away to a distance d from the original two charges?

QQ11

QQ22

25

1 2

0 0

1 14 4qQ qQU

d d

(superposition)(superposition)

dd

qq

dd

dd


Potential Energy of Many ChargesWhat is the total energy required to bring in three identical charges, from infinitely far away to the points on an equilateral triangle shown.

A) 0B) C) D) E)

QQ QQdd

QQ

27

2

0

14QU

d

2

0

12

4QU

d

2

0

134QU

d

2

0

164QU

d

dddd

Work to bring in second charge :Work to bring in second charge : dQW2

02 4

1

dQWW i

2

043

Work to bring in first charge: Work to bring in first charge: WW11 = 0 = 0

dQ

dQ

dQW

2

0

2

0

2

03 4

241

41

Work to bring in third charge :Work to bring in third charge :

dQU2

043


Potential Energy of Many ChargesSuppose one of the charges is negative. Now what is the total energy required to bring the three charges in infinitely far away?

A) 0B) C) D) E)

QQ QQdd

QQ

29

2

0

114QU

d

2

0

114QU

d

2

0

124QU

d

2

0

124QU

d

dddd

041

41 2

0

2

03

dQ

dQW

Work to bring in third charge :Work to bring in third charge :

dQWW i

2

041

dQU2

041

Work to bring in first charge: Work to bring in first charge: WW11 = 0 = 0

11

Work to bring in second charge :Work to bring in second charge : dQW2

02 4

1

22



31

““inserting another charge is going to increase the magnitude of the potential energy.” inserting another charge is going to increase the magnitude of the potential energy.” ““No matter what the sign is the potential energy would be a positive number minus a negative No matter what the sign is the potential energy would be a positive number minus a negative number minus another negative number. ”number minus another negative number. ”““the change in potential is found by adding another kqq/r term. this term is dependent on the the change in potential is found by adding another kqq/r term. this term is dependent on the sign of the new charge.“sign of the new charge.“

Two charges which are equal in magnitude, but opposite in sign, are place at equal distances from point A.

If a third charge is added to the system and placed at point A, how does the electric potential energy of the charge collection change?A. Increases B. decreases C. doesn’t changeD. The answer depends on the sign of the third charge



“The positive third charge will cancel out the The positive third charge will cancel out the negative charge.negative charge.““

““It doesn't matter what the sign is. Place the new It doesn't matter what the sign is. Place the new charge twice the distance from the - as the + charge twice the distance from the - as the + charge. It doesn't matter what the sign is because charge. It doesn't matter what the sign is because the U added to the system will now be zero.” the U added to the system will now be zero.”

““Adding a third charge that is opposite to at least Adding a third charge that is opposite to at least one other charge will cause a change in potential one other charge will cause a change in potential energy”energy”

34

LET’S DO THE CALCULATION !!LET’S DO THE CALCULATION !!

You start with two point charges separated by some distance. The charge of the first is positive. The charge of the second is negative and its magnitude is twice as large as that of the first.

Is it possible to find a place to which you can bring a third charge in from infinity without changing the total potential energy of the system?A. YES, as long as the third charge is positive B. YES as long as the third charge is negativeC. YES, no matter what the third charge is D. NO


Example: Potential Energy ChangesExample: Potential Energy Changes

A positive charge q is placed at x=0 and a negative charge -2q is placed at x=d. At how many different places along the x axis could another positive charge be placed without changing the total potential energy of the system?

37

qq -2q-2qxx

X=0X=0 X=dX=d

A)A) 00B)B) 11C)C) 22D)D) 33


Example: Potential Energy ChangesExample: Potential Energy Changes

At which two places can a positive charge be placed without changing the total potential energy of the system?

40

qq -2q-2qA B C D xxX=0X=0 X=dX=d

A)A) A & BA & BB)B) A & CA & CC)C) B & CB & CD)D) B & DB & DE)E) A & DA & D

Let’s calculate the positions of A and BLet’s calculate the positions of A and B


Lets work out where A is

43

qq -2q-2qA xxX=0X=0 X=dX=d

ddrr

drQq

rQqU

241

41

00

Set Set U = 0U = 0

drr

21

dr Makes Sense!Makes Sense!

Q is twice as far from -2q as it is from +qQ is twice as far from -2q as it is from +q


Lets work out where B is

46

qq -2q-2qB xx

X=0X=0 X=dX=d

d - rd - rrr

Setting Setting U = 0U = 0rdr

21

rdr 2

3dr

Makes Sense!Makes Sense!Q is twice as far from -2q as it is from +qQ is twice as far from -2q as it is from +q


Summary

q1 q2

rr

1 2q qU kr

For a pair of charges:For a pair of charges:

1 2q qU kr

For a collection of charges:For a collection of charges:

Sum upSum up for all pairsfor all pairs

Just evaluateJust evaluate

(We usually choose U = 0 to be where the charges are far apart)

physics 212 lecture 5, slide 1 physics 212 lecture 5 today's concept: electric potential energy...

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