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

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 5

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

q1Like signs repel

Electro-static Force

q2 q1

Opposite signs attractq2 q1

Unit 1, Slide 6

221

r

qqF

Coulomb’s Law

Electricity & Magnetism Lecture 1, Slide 7

22,12

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.

Coulomb’s Law

Electricity & Magnetism Lecture 1, Slide 8

22,12

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

Example 1.1 (forces between paper clips)

Unit 1, Slide 9

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 10

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

Electricity & Magnetism Lecture 1, Slide 11

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:

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

Electricity & Magnetism Lecture 1, Slide 12

F2,1

F3,1

F4,1

F1

1F

...1,41,31,2 FFF

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

F1F2,1

F3,1

F4,1

F1

q1

q2

q3

q4

F2,1

F3,1

F4,1

F1

q1

q2

q3

q4

Electricity & Magnetism Lecture 1, Slide 13

1F

...1,41,31,2 FFF

1F

...1,41,31,2 FFF

Electricity & Magnetism Lecture 1, Slide 14

qq

-Q +Q

+Q+Q

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

CheckPoint: Force from Four Charges

Four 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

What is the direction of horizontal force on Q?

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

x

y

3q

q qq

Q

Electricity & Magnetism Lecture 1, Slide 15

Example 1.3 (Force on charge)

Electricity & Magnetism Lecture 1, Slide 16

22,12

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 17

Charges are free to move on conductor

++

+ ++

+

+

+

+

+

+

+

+

+

+

+

Charges always on very edge of conductor