Unit 1: Coulomb’s Law Today’s Concepts - College of …s...Physics 2112 Unit 1: Coulomb’s Law Today’s Concepts: A) Coulomb’s Law B) Superposition Unit 1, Slide 1

Physics 2112

Unit 1: Coulomb’s Law

Today’s Concepts:

A) Coulomb’s Law

B) Superposition

Unit 1, Slide 1

Why are electrons fixed and stationary in plastics?

Nothing was difficult to understand. Videos were clear and concise.

Would like to see a variety of worked-out examples to strengthen

understanding.

The most difficult is listening to his voice.

donuts?

I think I understood this pre lecture for the most part.

HA AP Physics

i am confused about the forces relating to magnetism.

Feel ok about the check point. However was a bit confused in one of the

calculations, they didn't include one of charges and im not sure why. Would

be nice to do a few calculations in class. The lecture seemed fine.

You're going to be so proud of me! Like OMG. For the first time ever I actually

watched the whole pre-lecture and I actually thought about the Checkpoint

questions. Assuming I actually got these questions right, I didn't have trouble

with anything. :)

What we thought….

Electricity & Magnetism Lecture 2, Slide 2

Electric Charges

Electric charges come in two sign: + and -

Like sign charges repel, Opposite sign charges

attract.

Electric charge is “quantized”.

qe=1.602 X 10-19C

Charge of electron is exactly same as charge of

proton

Unit 1, Slide 3

Why?

Why?

Why?

How?!

Electric Charges

Electric charges is conserved

Unit 1, Slide 4

At Fermilab

-1 +1

anti-proton proton

Electric Charges

Tribo-electric

Series

Unit 1, Slide 5

Tend to lose electrons

when rubbed

Tend to gain electrons

when rubbed

When we place near the positively charged

glass rod, the ruler was attracted to it.

What will happen when it is placed near the

charged PVC rod?

A. It will be attracted to it

B. It will be repelled by it

C. There will be no effect

QUESTION

In our simulation, we have now rubbed the

sweater and the balloon, transferring charge

from one to the other. Both are pretty good

insulators. What can we say about the force

between the sweater and the balloon?

A. They will attract each other.

B. They will repel each other.

C. There will be no force between

them.

QUESTION

In our simulation, we have now rubbed the sweater

and the balloon, transferring charge from one to the

other, but the wall remained neutral. All three are

pretty good insulators. What can we say about the

force between the wall and the balloon?

A. They will attract each other.

B. They will repel each other.

C. There will be no force between them.

QUESTION

Conductors / Insulators

Conductors – charges are free to move

anywhere on the conductor

Insulators - charges remain where they

are place except in cases of “extreme”

force

Unit 1, Slide 9

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

r

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

q2

q2 q1

q1

Like signs repel

Electro-static Force

q2 q1

Opposite signs attractq2 q1

Unit 1, Slide 10

2

21

r

qqF

Coulomb’s Law


2,12

2,1

212,1 r̂

r

qqkF

k = 9 X 109 N m2/C2

Unit of Charge is Columb (C)

(big!) qe=1.602 X 10-19C

Charles-Augustin de Coulomb – French engineer who was a pioneer in torsion and

soil mechanics.

A hydrogen atom is composed of a nucleus containing a single

proton, about which a single electron orbits. When the electron

is in the lowest orbital position, the electric force between the

two particles is 2.3 X 1039 greater than the gravitational force!

How would we adjust the separation between the two particles

so the electric and gravitational forces are equal?

A) We must move the particles farther apart.

B) We must move the particles closer together.

C) It can’t be done at any distance.

QUESTION

Coulomb’s Law


2

2,12

2,1

212,1 r̂

r

qkqF

2,1F

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).

q2q1 2,1r

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

q1 q22,1F

2,1r

Our notation:

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

is the unit vector that points from 1 to 2. 2,1F

12r̂


Coulomb Force

What will the direction of the force be?

A) Attractive B) Repulsive

k 9 x 109 N m2 / C2

electron charge 1.6 x 10-19 Coulombs

NA 6.02 x 1023

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.

122

12

21 r̂r

qqkF

Question

Unit 1, Slide 15

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

A) Paperclip (1 g x g)

B) Text book (1 kg x g)

C) Truck (104 kg x g)

D) Aircraft carrier (108 kg x g)

E) Mt. Everest (1013 kg x g)

k 9 x 109 N m2 / C2

electron charge 1.6 x 10-19 Coulombs

NA 6.02 x 1023

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.

122

12

21 r̂r

qqkF

Example 1.1 (forces between paper clips)

Unit 1, Slide 16

Two 1 gram 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.

What is the force between the two clips?

Example 1.2 (forces between students)

Unit 1, Slide 17

What would the force be between two 80kg students sitting two meters apart if the charge of the proton were 10-10% greater than the charge of an electron?

CheckPoint: Forces on Two Charges


Two charges q = + 1 μC and Q = +10 μC are placed near

each other as shown in the figure below.

Which of the following diagrams best depicts the forces acting

on the charges:

CheckPoint Results: Forces on Two Charges


A) Since they are both positive they have to repel each other, and I would think the one with the stronger charge would repel more.

B) Just like a fly having the same amount of force impact on a bus that the bus has on the fly, two charges will have equal and opposite effects on each other in accordance with Newton's Third Law.

C) The force of 2 (+10 uC) on 1 (+1 uC) is 10 times greater than the force of 1 on 2 consequently causing charge 1 to become displaced at a much larger magnitude than charge 2.

Two charges, -Q and +2Q are placed a distance R apart.

The magnitude and direction of the force F on the -Q charge

is shown by the arrow. Which of the following arrows

represents the approximate magnitude and direction of the

force on the particle with the larger (+2Q) charge?

A.

C. D.

E.

B.

+2Q

-Q

Question

Two charges, -Q and +2Q are placed a distance R apart. The

magnitude and direction of the force F on the -Q charge is

shown by the arrow. Next, the –Q charge is changed to +2Q.

Which of the following arrows represents the approximate

magnitude and direction of the new force on the bottom +2Q?

Question

Two charges, -Q and +2Q are placed a distance R apart. The

magnitude and direction of the force F on the -Q charge is

shown by the arrow. The charges are then moved to a

separation distance of R/2. Which arrow’s direction and length

represents the force on the +2Q charge in this new position?e

new force on the +2Q charge?

Question

q1

q2

q3

q4

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

F2,1

F3,1

F4,1

F1

Superposition


F2,1

F3,1

F4,1

F1

1F

...1,41,31,2 FFF

What happens to the magnitude of Force on q1 if its sign is changed?

A) |F1| increases

B) |F1| remains the same

C) |F1| decreases

D) Need more information to determine


Question: Superposition

q1

q2

q3

q4

The direction of all forces changes by 180o – the magnitudes stay the same:

F2,1

F3,1

F4,1

F1

F2,1

F3,1

F4,1

F1

F2,1

F3,1

F4,1

F1

q1

q2

q3

q4

F2,1

F3,1

F4,1

F1

q1

q2

q3

q4


1F

...1,41,31,2 FFF

1F

- ...1,41,31,2 ---- FFF


qq

-Q Q

QQ

Case 1 Case 2

Compare the magnitude of the net force on q in the two cases.

A) |F1 | > |F2|

B) |F1 | |F2|

C) |F1 |< |F2|

D) Depends on sign of q

CheckPoint: Compare Forces

Case 1 Case 2


qq

-Q Q

QQ

Case 1 Case 2


A) |F1 | > |F2|

B) |F1 | |F2|

C) |F1 |< |F2|


F1

F2 0


A) No matter the sign of charge q, there will be an attractive and repulsive force in case

1 (same direction), and two forces (attractive or repulsive depending on the sign of the

charge on q) that cancel so that the net force on q is zero.

C) the distance between the two particles from charge q is the same and the quantity of

charge on +Q and -Q is the same. so the magnitude of the net force will be the same

in both cases.

D) I believe that if the sign of q is negative, the force on q will be less than if the sign of q

is positive, as there will be two repelling forces acting on it rather than one repelling

and one attracting force.


qq

-Q Q

QQ

Case 1 Case 2


A) |F1 | > |F2|

B) |F1 | |F2|

C) |F1 |< |F2|


F1

F2 0


D) because if the central charge is neutral there is no net force on either. If

the central charge isnt neutral, the net force would be greater in case 1.

Good point. From now on, if I refer to a q, you can assume |q| = 0

CheckPoint: Force from Four Charges

A positive charge Q is placed at the

origin. Four other positive charges are

placed on a circle in the x-y plane

centered on Q as shown. The top

charge is located on the y axis and

has a magnitude of 3q. The three

bottom charges are symmetric about

the y axis as shown and each has

magnitude q.

What is the direction of horizontal force on Q?

A) Fx > 0 B) Fx 0 C) Fx < 0

x

y

3q

q q

q

Q


CheckPoint Results: Force from Four Charges

What is the direction of horizontal force on Q?

A) Fx > 0 B) Fx 0 C) Fx < 0

x

y

3q

q q

q

Q










magnitude q.


What is the vertical force on Q?

A) Fy > 0 B) Fy 0 C) Fy < 0

x

y

3q

q q

q

Q

Question









magnitude q.


What is the vertical force on Q?

A) Fy > 0 B) Fy 0 C) Fy < 0

x

y

q q

q

Q

Question

A) The y distance between the bottom left and bottom right charges is less than the y

distance of the 3q on top, so the net force in the y direction would be upwards

B) because the magnitude of the 3q charge will equal the magnitude of the three q

charges.

C) all force of the 3q is directed along the negative y axis. some of the force exerted on Q

by two of the q charges is directed along the x axis. therefore the net force is along the

negative y axi

A positive charge Q is placed at the origin. Four

other positive charges are placed on a circle in

the x-y plane centered on Q as shown. The top

charge is located on the y axis and has a

magnitude of 3q. The three bottom charges are

symmetric about the y axis as shown and each

has magnitude q.

3q

Example 1.3 (Force on charge)


2

2,12

2,1

212,1 r̂

r

qkqF

q2

-30uC

+10uC

+25uC

q3q1

2m

2m

What is the force on q2?

Charge on a Conductor

Unit 1, Slide 34

Charges are free to move

on conductor

++

+ ++

+

+

+

+

+

+

+

+

+

+

+

Charges always on very

edge of conductor

Documents

Unit 1: Coulomb’s Law Today’s Concepts - College of …s...Physics 2112 Unit 1: Coulomb’s Law Today’s Concepts: A) Coulomb’s Law B) Superposition Unit 1, Slide 1