Electric Charge Chapter 21

Week-1

Chapter 21 Electric Charge

In this chapter we will introduce a new property of matter known as “electric charge” (symbol q ).

Moreover, we will describe the following properties of charge:

- Types of electric charge - Forces among two charges (Coulomb’s law) - Charge quantization - Charge conservation(21-1)

Probable First Observation ElectricityElectricity

Question

Pivot

motion

Rubber rod

Rubber rod

A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen

The charges on the two rods are ..

A. Since we treated both rods in the same way, they should be of the same type

B. ……. different typesC. I have no idea what you are asking for.D. Leave me alone … I’m napping!

If you rubbed the rods longer and/or harder, do you think the effect that you see would be

A. StrongerB. WeakerC. The same

If the two rods are brought closer together, the force acting between them will get …

A. StrongerB. WeakerC. The same

Empirically it was known since ancient times that if amber is rubbed on cloth, it acquires the property of attracting light objects such as feathers. This phenomenon was attributed to a new property of matter called “electric charge”. More experiments show that they are two distinct type of electric charge: Positive (color code : red) , and Negative (color code : black)

The names “positive” and “negative” were given by Benjamin Franklin.

When we rub a glass rod with silk cloth both objects acquire electric charge. The sign on the charge on the glass rod is defined as positive

In a similar fashion when we rub a plastic rod with fur both objects acquire electric charge. The sign on the charge on the plastic rod is defined as negative Q: Do we have enough information so as to determine the sign of all other charges in nature?

(21-2)

Q: Do we have enough information so as to be able to determine the sign of all other charges in nature? To answer this question we need one more piece of information.

Further experiments on charged objects showed that:

1. Charges of the same type (either both positive or both negative) repel each other (fig.a)

2. Charges of opposite type on the other hand attract each other (fig.b) The force direction allows us to determine the sign of an unknown electric charge. Charges of the same sign repel each

other. Charges of opposite sign attract each other

(21-3)

repulsive force

attractive force

What’s Going On? All of these effects involve rubbing two surfaces

together. Or pulling two surfaces apart. Something has “happened “to each of these objects. These objects have a new PROPERTY

Other properties are mass, color We call this NEW PROPERTY .………. ………

CHARGE. There seems to be two types of charge.

We call these two types of charge

PositiveNegative

An object without either a (+) or (-) charge is referred

to as being NEUTRAL.NEUTRAL.

Separation

An Example

Effect of Charge

In Benjamin Franklin’s day (18th century) it was assumed that electric charge is some type of weightless continuous fluid. Investigations of the structure of

atoms by Ernest Rutherford at the beginning of the 20th century revealed how matter is organized and also identified that charge of its constituents.

Atoms consist of electrons and the nucleus. Atoms have sizes 510-10 m Nuclei have sizes 510-15 m

The nucleus itself consists of two types of particles: protons and neutrons. The electrons are negatively charged The protons are positively charged, The neutrons are neutral (zero charge) Thus electric charge is a fundamental property of the elementary particles

(electrons, protons, neutrons) out of which atoms are made of. (21-5)

From whence this charge???

-+

Easily Removed

Mass and charge of atomic constituents (22-11)

Neutron (n) : Mass m = 1.67510-27 kg ; Charge q = 0

Proton (p) : Mass m = 1.67310-27 kg ; Charge q = +1.60210-19 C

Electron (e) : Mass m = 9.1110-31 kg ; Charge q = -1.60210-19 C

Note 1: We use the symbol “-e” and “+e” for the electron and proton charge, respectively. This is known as the elementary charge

Note 2: Atoms are electrically neutral. The number of electrons is equal to the number of protons. This number is known as “ atomic number ” (symbol: Z) The chemical properties of atoms are determined exclusively by Z

Note 3: The sum of the number of protons and the number of neutrons is known as the “ mass number ” (symbol: A)

Notation: Z= 92 = number of protons/electrons A = 235 = number of protons + neutrons

The atomic number Z = 92 defines the nucleus as that of a Uranium atom

23592U

(21-6)

Now that we identified the charge of the atomic constituents (electrons, protons, neutrons), it is clear that the net charge ofan object that contains electrons , protons

net

e p

QN N

Charge Quantization

, and neutrons

is given by: 0

Here and it is an integer. Thus the net charge is

This means that it cannot take any arbitrary value but only values

that

n

net e p n p e

p e

N

Q eN eN N e N N ne

n N N

quantized

are multiples of the elementary charge . The value of is small and thus in many large scale phenomena the "graininess" of electric charge is not apparent

e e

Ne

Np

Nn

(21-7)

silk

glass rod

silk

glass rod

-- --

++

++

Conservation of Charge

Net charge before = Net charge after

i fQ Q

(21-8)

Materials

Two kinds of materials: Insulators

Electrons and Protons are tightly bound to their positions. Hard to move them around.

Conductors Electrons are easily removed and moved around. Electrons are said to be MOBILE charges.

There are other kinds of materials that we will not discuss: semiconductors, semi-metals

+++

++

Ways to charge an object

Transfer Direct transfer Polarization Induction

A conductor can be charged using the procedureshown in the fig.a and fig.b. In fig.a a conductor issuspended using an insulating thread. The conductoris initially un

Charging a conductor by induction

charged. We then approach the conductorwith a negatively charged rod. The negative charges on the rod are fixed because plastic is an insulator. These repel the conduction electrons of the conductorwhich end up at the right end of the rod. The right endof the rod has an electron deficiency and thus becomespositively charged. In fig.b we provide a conductingpath to ground (e.g. we can touch the conductor).As a result the electrons escape to the ground. If we remove the path to the ground and the plastic rodthe conductor remains positively charged.

The induced charge on the conduNote 1 : ctor has theopposite sign of the charge on the rod.

The plastic rod can be used repeatedlyNote 2 :

Fig.a

Connection to ground

---

Fig.b

(21-11)

Neutral Object - POLARIZATION

Positive charge attracts negative charges.Rod becomes “polarized.Negative end is closer to positive chargeDistance effect causes attraction.

Induction

Polarize

Ground

Remove Ground

Positive !

m1m2

r

F1

m2

m11 2

1 2 mmF Gr

0F

Q1Q2

r

F1

Q2Q1

1 21 2

1 4 o

Q QF

r 1 0F

1 2

2

1

1

2

2

The gravitational force that a uniform shell of mass exerts a particle of mass

that is outside the shell is given the the equation:

It is as if the shell's mass were all concetra e

t

mmF G

m m

mr

1 2

d at the shell center. If is inside the shell, the net force exerted by is zero. Because of the similarity between Newton's gravitational law and Coulom's law,the same is true for the elec

tric

m m

2

1 1 1 2

11

21 12

force exerted by a spherical shell of charge on a point charge . If is outside the shell t

1

hen the force exerted by is:

If is inside the shell then the force 4

0o

Q Q

QQ Q F

F Fr

Q

Q

(21-15)

Forces Between Charges

Q1 Q2 Attract Repel

+ + X

+ - X

- + X

- - X

Coulomb’s Law – Force between charges

The force between two charges is proportional to the product of the two charges and inversely proportional to the square of the distance between them.

The force acts along the line connecting the two charges.

0

221

221

02

21

41

41

k

rqqk

rqq

rqqF

Remember

Coulomb’s Law

229

0

221

0

/1094

14

1

CNmxk

rqq

unit

rF

The Unit of Charge is calledTHE COULOMB

Smallest Charge: e ( a positive number) 1.6 x 10-19 Coul.

electron charge = -eProton charge = +e

The net electric force exerted by a group ofcharges is equal to the vector sum of the contributionfrom each charge.

Coulomb's law and the Principle of Superposition

1 1 2 3

12 13 1

1 12 13

2 3

1

For example the net force exerted on by and is equal to:

Here and are the forces exerted on by and , respectively. In general the force exerted

on

FF q q q

F F q q q

F

q

F

1 12 13 14 1 12

12 13

by n charges is given by the equation:

...

One must remember that , , ...are vectors and thuswe must use use vector addition. Inthe example of fig.f we have

n

n ii

F F F F F F

F F

:

(21-14)

1 12 14 F F F

m1m2

r

F1

m2

m11 2

1 2 mmF Gr

0F

Q1Q2

r

F1

Q2Q1

1 21 2

1 4 o

Q QF

r 1 0F

1 2

2

1

1

2

2

The gravitational force that a uniform shell of mass exerts a particle of mass

that is outside the shell is given the the equation:

It is as if the shell's mass were all concetra e

t

mmF G

m m

mr

1 2

d at the shell center. If is inside the shell, the net force exerted by is zero. Because of the similarity between Newton's gravitational law and Coulom's law,the same is true for the elec

tric

m m

2

1 1 1 2

11

21 12

force exerted by a spherical shell of charge on a point charge . If is outside the shell t

1

hen the force exerted by is:

If is inside the shell then the force 4

0o

Q Q

QQ Q F

F Fr

Q

Q

(21-15)

Three point charges are located at the corners of an equilateral triangle as shown in the Figure. Calculate the resultant electric force on the 7.00-μC charge.

Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. As shown in the Figure, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?