Unit 1: Coulomb’s Law Today’s Concepts

Physics 2112

Unit 1: Coulomb’s Law

Today’s Concepts:

A) Coulomb’s Law

B) Superposition

Unit 1, Slide 1

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 2

Why?

Why?

Why?

How?!

Electric Charges

Electric charges is conserved

Unit 1, Slide 3

At Fermilab

-1 +1

anti-proton proton

Electric Charges

Tribo-electric

Series

Unit 1, Slide 4

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 8

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 9

2

21

r

qqF

Coulomb’s Law

Electricity & Magnetism Lecture 1, Slide 10

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.

Example 1.1 (Force on charge)


2

2,12

2,1

212,1 r̂

r

qkqF

-30uC+25uC

q3q1

2m

2m

What is the electro-static force on q3?

25X10-6 kg30 X10-6 kg

What is the gravitational force on q3?

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

Example 1.2 (forces between students)

Unit 1, Slide 13

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?

Question

Unit 1, Slide 14

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

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 big charge is going to really want to push away the smaller charge, therefore the vector for the smaller "mass" is larger than on the larger "mass".

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|

C) D) Depends on sign of q

CheckPoint: Compare Forces

Case 1 Case 2


qq

-Q Q

QQ

Case 1 Case 2

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.

B) the bigger force exerted on q is case 2 because the net force exerted in case 1 is 0.

C) Although Case one will be repelled and two will be attracted, the magnitude of the

forces will be the same

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

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

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 24

Charges are free to move

on conductor

++

+ ++

+

+

+

+

+

+

+

+

+

+

+

Charges always on very

edge of conductor

Unit 1: Coulomb’s Law Today’s Concepts

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