Physics 212 Lecture 1, Slide 1 Physics 212 Lecture 1 Today's Concepts: a) Coulomb’s Law b)...

Physics 212 Lecture 1, Slide Physics 212 Lecture 1, Slide 11

Physics 212Physics 212Lecture 1Lecture 1

Today's Concepts:Today's Concepts:a) Coulomb’s Lawa) Coulomb’s Lawb) Superpositionb) Superposition

0202

Original: Mats SelenOriginal: Mats SelenModified: W.GeistModified: W.Geist

• My web page: http://facstaff.gpc.edu/~wgeist/ • Homework: www.masteringphysics.com 20% Pre-class assignments are due before class!• 3exams + 1 final: 75%• I<clickers: 5%• Book: P.A Tipler, G. Mosca "Physics for Scientists and engineers", 6'th edition.

• Mc Dermott et al: Tutorials in Introductory physics Check the web page and print them out before class!

• Get your i-clickers from the bookstore.

http://facstaff.gpc.edu/~wgeist/

http://www.masteringphysics.com/

Warm up exercise

Which force is larger?A) the force of the apple on the earth.B) The force of the earth on the apple.C)The same

Newton’s law of gravity:

Force by earth on apple = Force by apple on earth


2

apple earthearth on apple apple on earth

a e

m mF G F

r


Coulomb’s Law:Coulomb’s Law:

qq11qq22

The force on a charge due to another charge The force on a charge due to another charge proportional to the product of the charges and inversely proportional to the product of the charges and inversely proportional to the separation squared. proportional to the separation squared.

1 22

q qF

r

rr

qq11qq22

The force is always parallel to a line connecting the The force is always parallel to a line connecting the charges, but the direction depends on the signs of the charges, but the direction depends on the signs of the charges:charges:

qq11qq22

Opposite signs attractOpposite signs attract

qq11qq22

Likes signs repelLikes signs repel

0707


Pith ballsPith balls

Take two pith balls and charge them Take two pith balls and charge them both with a plastic rod. After both with a plastic rod. After you charged them they will:you charged them they will:

A)A) Attract each-otherAttract each-otherB)B) Repel each-otherRepel each-otherC)C) Either – it depends on the material of the clothEither – it depends on the material of the cloth

1010


If the If the samesame thing is done to both balloons thing is done to both balloons they will acquire the they will acquire the samesame sign charge. sign charge.

They will repel !They will repel !

++++

++++

++++

++++

Pith ballsPith balls

1111

Conductors and InsulatorsConductors and Insulators

Conductor is an object where charge moves along or through.

Insulator is an object where

the charge does not move.

Notice: You can charge the glass and plastic, hence an insulator can be charged, but the charge is stuck on the surface and cannot move.

Conductors and InsulatorsConductors and Insulators Where is the charge on the

conductor?• Charge is transferred to the box

by contact.• Charge moves freely through

metal.• Like charges repel each other.• Consequently, charge placed on a

metal will quickly spread as far as possible and will charge the entire metal surface. This is in contrast to the charge placed on an insulator. The time for the charge to spread out on a conductor is "instantaneous" as far as simple experiments are concerned.

Polarization of a metalPolarization of a metal

Aluminum Aluminum foilfoil

Why is the aluminum foil lifted off Why is the aluminum foil lifted off the ground?the ground?


Why is the aluminum foil lifted off Why is the aluminum foil lifted off the ground?the ground?

Coulomb’s Coulomb’s Law:F~1/rLaw:F~1/r22


FF+on-+on- -F -F+on+ +on+ > mg> mg

FF+on-+on-

FF+on++on+

Induction

AA BB---------- AA BB --

------

++++

++++

----------AA BB --

------

++++++

++

BB--

-- ----

AA++++++

++

Two metal spheres mounted on insulating stands.Two metal spheres mounted on insulating stands.1.1. Make the spheres touchMake the spheres touch2.2. Bring a charged rod near one of the spheresBring a charged rod near one of the spheres3.3. Separate the spheresSeparate the spheres4.4. Remove the charged rodRemove the charged rod

Clicker Question: Induction

A positively charged object is placed close to a conducting object attached to an insulating glass pedestal (a). After the opposite side of the conductor is grounded for a short time interval (b), the conductor becomes negatively charged (c). Based on this information, we can conclude that within the conductor:

1. both positive and negative charges move freely.2. only negative charges move freely.3. only positive charges move freely.4. We can’t really conclude anything.

- - - - - -- ---

++++

++++

++++

++++


Coulomb’s LawCoulomb’s Law

qq11 qq221,2r

1 21,2 1,22

1,2

ˆkq q

F rr

1414

Our notation Our notation

is the force is the force byby 1 1 onon 2 (think “ 2 (think “by-on by-on ”) ”)

is the vector that points is the vector that points fromfrom 1 1 toto 2. 2.

1,2

F

12

r

Examples Examples If the charges have the same sign, the force by charge

1 on charge 2 would be in the direction of r12 (to the right) 1,2

F

If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direction of r12 (left)

qq11 qq22

1,2r

1,2

F


Example: Coulomb Force

• Two paperclips are separated by 10 meters. Then you remove 1 electron from each atom on the first paperclip and place it on the second one.

1 2122

12

ˆqq

F k rr

k= 9 x 10k= 9 x 1099 N m N m22 / C / C22

electron charge = 1.6 x 10electron charge = 1.6 x 10-19-19 Coulombs Coulombs

NNAA = 6.02 x 10 = 6.02 x 102323

What will the direction of the force be? What will the direction of the force be?

A) Attractive A) Attractive B) Repulsive B) Repulsive

1616




1 2122

12

ˆqq

F k rr

mmAA=27=27

k= 9 x 10k= 9 x 1099 N m N m22 / C / C22


NNAA = 6.02 x 10 = 6.02 x 102323

Which weight is closest to the approximate force between those paperclips (recall that weight = mg, g = 9.8 m/s2)?

A)A) Paperclip (1g x g)Paperclip (1g x g)

B)B) Text book (1kg Text book (1kg x gx g))

C)C) Truck (10Truck (1044 kg kg x gx g))

D)D) Aircraft carrier Aircraft carrier (10(1088 kg x g) kg x g)

E)E) Mt. Everest (10Mt. Everest (101414 kg kg x gx g))

2020




1 2122

12

ˆqq

F k rr

k= 9 x 10k= 9 x 1099 N m N m22 / C / C22


NNAA = 6.02 x 10 = 6.02 x 102323

Number of electrons on a 1g aluminum: N = NNumber of electrons on a 1g aluminum: N = NAA/27/27

F = k N e N e /100mF = k N e N e /100m2 2 = 9 x 1.6 x 1.6 x 6/27 x 6/27 x 10 = 9 x 1.6 x 1.6 x 6/27 x 6/27 x 109+23+23-19-19-2 9+23+23-19-19-2 = = 10101515 N N

F(MtEverest) = 9.8x 10F(MtEverest) = 9.8x 1014 14 N N

2020


The forces are equal and opposite. This is due to The forces are equal and opposite. This is due to Newton's third law. Newton's third law.

2222


Charges on StringsTwo balls of equal mass are suspended from the ceiling with non-conducting wire. One ball is given a charge +3q and the other is given a charge +q.

g+q+3q

Which of the following best represents the equilibrium positions?

(b)(a)

+3q+q

(c)

+3q

+q

+3q +q

2525


Charges on StringsWhich best represents the equilibrium position?

• Remember Newton’s Third Law!• F31 = -F13

+3q+q +3q

+q

+3q +q

(b)(a) (c)

2626


The forces between Q1 and Q3 are equal and The forces between Q1 and Q3 are equal and opposite, satisfying Newton's third law. opposite, satisfying Newton's third law.

2727


Superposition:Superposition:

qq11

qq22

If there are more than two charges present, the total If there are more than two charges present, the total force on any given charge is just the force on any given charge is just the vector sumvector sum of the of the forces due to each of the other charges:forces due to each of the other charges:

qq33

qq44

FF2,12,1

FF3,13,1

FF4,14,1

FF11

FF2,12,1

FF3,13,1

FF4,14,1

FF11

2,1 3,1 4,1 ...F F F

1F

3030


What happens to Force on qWhat happens to Force on q11 if its sign is changed if its sign is changed

qq11

qq22

qq33

qq44

A)A) |F|F11| increases| increases

B)B) |F|F11| remains the same| remains the same

C)C) |F|F11| decreases| decreases

D)D) Need more information to determineNeed more information to determine

Superposition ACTSuperposition ACT

3232


qq11

qq22

The The directiondirection of all forces changes by 180 of all forces changes by 180oo – the – the magnitudesmagnitudes stay the stay the same:same:

qq33

qq44

FF2,12,1

FF3,13,1

FF4,14,1

FF11

FF2,12,1

FF3,13,1

FF4,14,1

FF11

2,1 3,1 4,1 ...F F F

1F

3333

qq11

qq22

qq33

qq44

FF2,12,1

FF3,13,1

FF4,14,1

FF11

FF2,12,1

FF3,13,1

FF4,14,1

FF11

2,1 3,1 4,1 ...F F F

1F


Coulomb Force simulationCoulomb Force simulation

http://www.hep.uiuc.edu/home/mats/flash/Super.html


Since there are both a positive and negative charge in Case 2, some of the force will be cancelled out when the vectors are summed. In Case 1 and 3 the magnitude will be the same whether the charge is positive or negative.

simulationsimulation

PreflightPreflight 33

3535

http://www.hep.uiuc.edu/home/mats/flash/dipole_potential.html


If Q4 was positive, the two + charges would result in a vector pointing in the If Q4 was positive, the two + charges would result in a vector pointing in the direction exactly opposite and equal in magnitude to the vector pointing toward direction exactly opposite and equal in magnitude to the vector pointing toward the negative charge. The same is true is Q4 was negative. the negative charge. The same is true is Q4 was negative.

AABBCC

3838


ExampleFour charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring

qqqq qq

3q3qWhat is horizontal force on Q?What is horizontal force on Q?

A) FA) Fxx > 0 B) F > 0 B) Fxx = 0 C) F = 0 C) Fxx < 0< 0

xx

yy

QQ

4141



qqqq qq

3q3qWhat is vertical force on Q, if Q What is vertical force on Q, if Q has same sign charge as q?has same sign charge as q?

A) FA) Fyy > 0 B) F > 0 B) Fyy = 0 C) F = 0 C) Fyy < 0< 0

xx

yy

QQ

4141


SolutionFour charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring

qqqq qq

3q3q

QQ

Case 1: Q same sign charge as qCase 1: Q same sign charge as q xx

yy

4747

==



qqqq qq

3q3qWhat is vertical force on Q, if Q What is vertical force on Q, if Q has opposite sign charge as q?has opposite sign charge as q?

A) FA) Fyy > 0 B) F > 0 B) Fyy = 0 C) F = 0 C) Fyy < 0< 0

xx

yy

QQ

4141


SolutionFour charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring

qqqq qq

3q3q

QQ

Case 2: Q opposite sign charge as Case 2: Q opposite sign charge as qq

xx

yy

4747

==


Try using our Coulomb Force simulationTry using our Coulomb Force simulation

http://www.hep.uiuc.edu/home/mats/flash/Super.html

++++

++++

++++

+Q+Q+Q+Q+Q+Q

++ +q+q

θθ θθ

ss

ssss

For the following charge distribution, For the following charge distribution, find the net Coulomb force on the +q find the net Coulomb force on the +q

chargecharge..(Q=10nC, q=1nC, s=10cm, (Q=10nC, q=1nC, s=10cm, θθ=30=3000 ) )

A)F=A)F= 2.5 x 10 2.5 x 10-6-6N N B)F=B)F= 5.5 x 10 5.5 x 10-6-6N N C)F=C)F= 0N 0ND)F=D)F= 0.5 x 10 0.5 x 10-6-6N N

Solution: See lect 02Solution: See lect 02

Physics 212 Lecture 1, Slide 1 Physics 212 Lecture 1 Today's Concepts: a) Coulomb’s Law b)...

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