Physics 121: Electricity & Magnetism – Lecture 2 Electric Charge

 Many similar experiments of all kinds led Benjamin Franklin around 1750 to the conclusion that there are two types of charge, which he called positive and negative..  You can make the

Physics 121: Electricity & Magnetism – Lecture 2

Electric Charge

Dale E Gary Wenda Cao

NJIT Physics Department

(balloons, comb &

paper, shock from a

door knob)

 Uses—photocopying,

ink-jet printing

Static Charge

1 How can I demonstrate static charge using

an inflated balloon?

A Pop it The sound it makes is due to static charge.

B Rub it on cloth, rug, or hair, then it will stick to a

wall.

C Rub it on a metal surface, then use it to pick up

bits of paper.

D Drop it and time its fall If it falls slower than a

rock, it is affected by static charge.

E Let the air out slowly It will be larger than its

original size due to static charge.

Glass Rod/Plastic Rod

 A glass rod rubbed with silk gets a positive

charge

 A plastic rod rubbed with fur gets a negative

charge

 Suspend a charged glass rod from a thread, and

another charged glass rod repels it

 A charged plastic rod, however, attracts it

 This mysterious force is called the electric force

 Many similar experiments of all kinds led

Benjamin Franklin (around 1750) to the

conclusion that there are two types of charge,

which he called positive and negative.

 He also discovered that charge was not created

by rubbing, but rather the charge is transferred

from the rubbing material to the rubbed object,

or vice versa

Forces Between Charges

Like charges repel each other

Opposite charges attract each other

 This is a device that can visually

show whether it is charged with

static electricity

the ends, and since like charges

repel, they exert a force sideways

 You can make the deflection arm

move by adding either positive or

negative charge.

 BUT, we seem to be able to make

it move without touching it.

The Atom

 We now know that all atoms are made of positive charges in the nucleus, surrounded by a cloud of tiny electrons.

Proton Electron

More accurate picture of the atom—the Helium atom

Proton charge e, electron charge e

where e = 1.6021019 C

Neutron

The Atom

 We now know that all atoms are made of positive charges in the

nucleus, surrounded by a cloud of tiny electrons.

Proton Electron

Proton charge e, electron charge e

where e = 1.6021019 C

Neutron

 Atoms are normally neutral,

meaning that they have exactly the same number of protons as they do electrons.

 The charges balance, and the

atom has no net charge.

2 Which type of

charge is easiest to remove from an

atom?

A Proton

B Electron

A Positive

B Negative

 In fact, protons are VASTLY more difficult to remove, and for all

practical purposes it NEVER happens except in radioactive

materials In this course, we will ignore this case Only electrons can be removed.

If we cannot remove a proton, how

do we ever make something charged negatively? By adding an

“extra” electron.

Glass Rod/Plastic Rod Again

glass/plastic rod experiments

grabs them away from the glass atoms, so after

rubbing the glass becomes positively charged

and the silk becomes negatively charged

 Plastic has the opposite tendency It easily

grabs electrons from the fur, so that it becomes

positively charged while the fur becomes

negatively charged

The ability to gain or lose electrons through

rubbing is called Triboelectricity.

Tribo means rubbing

Triboelectric Series

asbestos rabbit fur glass hair nylon wool silk paper cotton hard rubber synthetic rubber polyester styrofoam orlon saran polyurethane polyethylene polypropylene polyvinyl chloride (PVC pipe)

teflon silicone rubber

Most Positive (items on this end lose electrons)

Most Negative (items on this end steal electrons)

Insulators and Conductors

 Both insulators and conductors can be

charged.

 The difference is that

 On an insulator charges are not able to move

from place to place If you charge an insulator, you are typically depositing (or removing)

charges only from the surface, and they will stay where you put them.

 On a conductor, charges can freely move If you try to place charge on a conductor, it will quickly spread over the entire conductor.

Insulator

Insulators and Conductors

4 Which of the following is a good

Metals and Conduction

 Notice that metals are not only good electrical conductors, but

they are also good heat conductors, tend to be shiny (if polished), and are maleable (can be bent or shaped).

 These are all properties that come from the ability of electrons to

Van de Graaf Generator

 Rubber band steals electrons

 Wire “brush” steals electrons

from rubber band

 Positively charged glass steals

electrons from upper brush

 Sphere (or soda can) becomes

positively charged—to 20,000 volts!

Electric Force and Coulomb’s

Law

 We can measure the force of attraction or repulsion between charges,

call them q1 and q2 (we will use the symbol q or Q for charge).

 When we do that, we find that the force is proportional to the each of the charges, is inversely proportional to the distance between them,

and is directed along the line between them (along r).

 In symbols, the magnitude of the force is where k is

some constant of proportionality

 This force law was first studied by Coulomb in 1785, and is called

Coulomb’s Law The constant k = 8.98755109 N m2/C2 is the Coulomb constant

r

q q k

F 

Electric Force and Coulomb’s

Law

 Although we can write down a vector form for the force, it is easier

to simply use the equation for the magnitude, and just use the

“like charges repel, opposites attract” rule to figure out the

direction of the force

 Note that the form for Coulomb’s Law is exactly the same as for

gravitational force between two masses

 Note also that the mass is an intrinsic property of matter

Likewise, charge is also an intrinsic property We only know it

exists, and can learn its properties, because of the force it exerts

 Because it makes other equations easier to write, Coulomb’s

constant is actually written

where  = 8.851012 C2/N-m2 is called the permittivity constant

2 2 1

r

m m G

F 

q m

k G



There is only one “sign”

of mass, only attraction.

4

1

r

q q F





Full form of Coulomb’s Law

Spherical Conductors

 Because it is conducting, charge on a metal sphere will go

everywhere over the surface.

 You can easily see why, because each of the charges pushes on the others so that they all move apart as far as they can go

Because of the symmetry of the situation, they spread themselves out uniformly.

 There is a theorem that applies to this case, called the shell

theorem, that states that the sphere will act as if all of the charge were concentrated at the center.

These two situations are the same Note, forces are equal and opposite

Insulators and Conductors

5 Two small spheres are charged with equal and

opposite charges, and are placed 30 cm apart Then the charge on sphere 1 is doubled Which diagram could be considered to show the

Case of Multiple Charges

 You can determine the force on a particular charge by adding up all of the forces from each charge.

Forces on one charge due to a number of other charges

Charges in a Line

 q

2

q

6 Where do I have to place the + charge in

order for the force to balance, in the

C On the line between the two negative

charges, but closer to the 2q charge.

D On the line between the two negative

charges, but closer to the q charge.

E There is no location that will give force

balance.

Let’s Calculate the Exact

Location

 Force is attractive toward both negative charges, hence

could balance

 Need a coordinate system, so choose total distance as L,

and position of + charge from q charge as x.

 Force is sum of the two force vectors, and has to be zero,

so

 A lot of things cancel, including Q, so our answer does not

depend on knowing the + charge value We end up with

 Solving for x, , so slightly less than

0 )

(

2

2 2

L

qQ k

F F F

2 2

1 )

(

2

x x

x L

 Charge is an intrinsic property of matter

 Charge comes in two opposite senses, positive and negative

 Mobil charges we will usually deal with are electrons, which can be removed from an atom to make positive charge, or added to an atom

to make negative charge A positively charged atom or molecule can also be mobil

 There is a smallest unit of charge, e, which is e = 1.6021019 C

Charge can only come in units of e, so charge is quantized The unit

of charge is the Coulomb

 Charge is conserved Charge can be destroyed only in pairs (+e and –

e can annihilate each other) Otherwise, it can only be moved from place to place

 Like charges repel, opposite charges attract

 The electric force is give by Coulomb’s Law:

 Materials can be either conductors or insulators

 Conductors and insulators can both be charged by adding charge, but

charge can also be induced.

 Spherical conductors act as if all of the charge on their surface were concentrated at their centers

2

2 1 0

4

1

r

q q F



