Physics 121: Electricity & Magnetism – Lecture 2

Electric ChargeDale E. GaryWenda Cao

NJIT Physics Department

September 5, 2007

Electricity in Nature Most dramatic natural

electrical phenomenon is lightning.

Static electricity (balloons, comb & paper, shock from a door knob)

Uses—photocopying, ink-jet printing

September 5, 2007

Static Charge1. 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.

September 5, 2007

Demonstrations of Electrostatics

BalloonGlass rod/silkPlastic rod/furElectroscopeVan de Graaf Generator

September 5, 2007

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.

September 5, 2007

Forces Between ChargesWe observe that

Like charges repel each other

Opposite charges attract each other

September 5, 2007

Electroscope This is a device that can visually

show whether it is charged with static electricity.

Here is an example charged positive.

Notice that the charges collect near 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.

What is happening?

Positively charged rod

- - - - - -

Electrostatic Induction

September 5, 2007

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 -ewhere e = 1.60210-19 C

Neutron

September 5, 2007

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 -ewhere e = 1.60210-19 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. ProtonB. Electron

September 5, 2007

The Atom

Proton charge +e, electron charge -ewhere e = 1.60210-19 C

3. If we remove an electron, what is the net charge on the atom?

A. PositiveB. 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.

September 5, 2007

Glass Rod/Plastic Rod Again We can now interpret what is happening with

the glass/plastic rod experiments. Glass happens to lose electrons easily, and

silk 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

September 5, 2007

Triboelectric Seriesasbestos 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)

September 5, 2007

Conductor

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

September 5, 2007

Insulators and Conductors4. Which of the following is a good

conductor of electricity?A. A plastic rod.B. A glass rod.C. A rock.D. A wooden stick.E. A metal rod.

September 5, 2007

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 move easily.

Path of electronin a metal

This iron atom (26 protons, 26 electrons) has two electrons in its outer shell, which can move from one iron atom to the next in a metal.

September 5, 2007

Van de Graaf Generator Rubber band steals electrons

from glass Glass becomes positively

charged Rubber band carries electrons

downward Positively charged glass

continues to rotate 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!

September 5, 2007

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 = 8.98755109 N m2/C2 is the Coulomb constant.

rq1 q2

q1 q2

221

rqq

kF

September 5, 2007

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 e0 = 8.8510-12 C2/N-m2 is called the permittivity constant.

221

rmmGF

qmkG

Note BIG difference,

There is only one “sign”of mass, only attraction.

041e

k2

21

041

rqq

Fe

Full form of Coulomb’s Law

September 5, 2007

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

September 5, 2007

Insulators and Conductors5. 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 correct forces? -q

A.

B.

C.

D.

E.

2q

September 5, 2007

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

September 5, 2007

Charges in a Line

-q

-2q

6. Where do I have to place the + charge in order for the force to balance, in the figure at right?

A. Cannot tell, because + charge value is not given.

B. Exactly in the middle between the two negative charges.

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.

September 5, 2007

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 half-way between.

-q

-2q

x

L

0)(

22221 -

-+

xqQk

xLqQkFFF

22

1)(

2xxL

-

22)(2

2

-

-

xxL

xxL

LLx 412.021

+

September 5, 2007

Summary 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 = 1.60210-19 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.

221

041

rqq

Fe