Electric Charge: Properties, Conservation, and Coulomb's Law, Study notes of Physics

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PH 222-3A Spring 2010

ELECTRIC CHARGE

Lecture 1

Chapter 21

(Halliday/Resnick/Walker, Fundamentals of Physics 8th^ edition)

1

Chapter 21

Electric Charge

In this chapter we will introduce a new property of

matter known as “electric charge” (symbol q ).

We will explore the charge of atomic constituents.

Moreover, we will describe the following properties of

charge:

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

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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.

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repulsive force

attractive force

The recipe is as follows: We charge a glass rod by rubbing it with silk cloth. Thus we know that the charge on the glass rod is positive. The rod is suspended in such a way so that it can keep its charge and also rotate freely under the influence of a force applied by charge with the unknown sign. We approach the suspended class rod with the new charge whose sign we wish to determine. Two outcomes are possible. These are shown in the figure to the left: Fig. a : The two objects repel each other. We then conclude that the unknown charge has a positive sign. Fig. b : The two objects attract each other. We then conclude that the unknown charge has a negative sign.

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Mass and Charge of Atomic Constituents

Neutron (n) : Mass m = 1.675 10 -27^ kg; Charge q = 0

Proton (p) : Mass m = 1.673 10 -27^ kg; Charge q = +1.602 10 -19^ C

Electron (e) : Mass m = 9.11 10 -31^ kg; Charge q = -1.602 10 -19^ C

Note 1: We use the symbols “-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 the “ 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.

235 92 U

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The electrical forces between two neutral atoms

tend to cancel

• Each electron in one atom is attracted by the protons in the nucleus of the other atom and simultaneously it is repelled by the equal number of electrons of that atom.
• Likewise, the electric forces between two neutral macroscopic bodies separated by some distance tend to cancel
• The cancellation of the electric forces between neutral macroscopic bodies explains why we do not see large electric attractions or repulsions between the macroscopic bodies, even though the electric forces between individual e and p are much stronger than the gravitational forces. 8

net

Now that we have identified the charge of the atomic constituents

(electrons, protons, neutrons), it is clear that the net charge of

an object that contains e electrons , p pr

Q

N N

Charge Quantization

net

otons , 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 value

n

e p n p e

p e

N

Q eN eN N e N N ne

n N N quantized.

s that 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

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silk

glass rod

silk

glass rod

- -

+

+

+ +

Conservation of Charge Consider a glass rod and a piece of silk cloth (both uncharged) shown in the upper figure. If we rub the glass rod with the silk cloth we know that positive charge appears on the rod (see lower figure). At the same time an equal amount of negative charge appears on the silk cloth, so that the net rod-cloth charge is actually zero. This suggests that rubbing does not create charge but only transfers it from one body to the other, thus upsetting the electrical neutrality of each body. Charge conservation can be summarized as follows: In any process the charge at the beginning equals the charge at the end of the process.

Net charge before = Net charge after

Qi Qf 11

Charge Conservation

• The electric charge is a conserved quantity: In any reaction involving charged particles, the total charges before and after the reaction are always the same. No reaction that creates or destroys net electric charge has ever been discovered. Conservation of charge in chemical reactions in a lead–acid automobile battery.

SO 4 - - and H+

PbO 2 Pb

The reaction releases electrons at the lead plate, electrons are absorbed at the lead dioxide plate.

e Plates of lead and lead dioxide are immersed in an electrolytic solution of sulfuric acid.

Lead Plate: Pb + SO 4 - -^ PbSO 4 + 2[electron]

Charges: 0 + (-2e) 0 + (-2e)

Lead-dioxide Plate: PbO 2 + 4H+^ + SO 4 - -^ + 2[el] PbSO 4 + 2H 2 O

Charges: 0 + 4e + (-2e) + (-2e) 0 + 0 13

Problem. Consider the following hypothetical reactions involving the collision between a high energy proton (from an accelerator) and a stationary proton (in the nucleus of a hydrogen atom serving as a target).

1. p + p n + n + π +

2. p + p n + p + π o

3. p + p n + p + π +

4. p + p p + p + π o^ + π o

5. p + p n + p + π o^ + π –

Which of these reactions are impossible, because they violate the conservation of charge?

1. e + e 0 + 0 + e } Charge is not conserved, reaction is impossible

2. e + e 0 + e + 0 } Charge is not conserved, reaction is impossible

3. e + e 0 + e + e } Charge is conserved

4. e + e e + e + 0 + 0 } Charge is conserved

5. e + e 0 + e + 0 + (-e) } Charge is not conserved, reaction is impossible

Where p = proton n = neutron π +^ = positively charged pion (+e) π o^ = neutral pion (e) π -^ = negatively charged pion (-e)

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16

The electrons are held inside the metal in much the same way as particles of a gas are held inside a container. => Electrons in metals form free electron gas

Conductors

Metals Electrolytes or liquid Ionized gases

conductors containing plasma

ions of impurity. Solution of salt in water Na+^ , Cl- Ordinary gases are insulators. Ionization of a gas occurs whenever the gas molecules are subjected to large electric forces, that produce a sudden catastrophic ionization of the gas.

Gases containing a mixture of ions and free electrons

Insulator or Dielectric. Energy level diagram.

Na+^ Cl-^ + - + -

The ions of dielectric crystals hold their electrons strongly and so a sample doesn’t contain free electrons. Free electrons can appear only when we ionize our ions and provide electrons with KE > Potential energy of attraction to the ions. This process can be described with the help of an energy level diagram.

Conduction band

/ / / / / / /

Forbidden band 3 15 eV

---

e e e e e e

Valence band

Insulator

VB

CB < 0.5eV

Metal (conductor) 1eV = 1.6 x 10-19^ J

CB

VB

3eV

Semiconductor 17

Frictional electricity. Charging by rubbing.

++++++

---

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A conductor can be charged using the procedure shown in fig. and fig.. In fig. a conductor is suspended using an insulating thread. The conductor is initially unc

a b a

Charging a Conductor by Induction

harged. We then approach the conductor with a negatively charged rod. The negative charges on the rod are fixed because plastic is an insulator. These repel the conduction electrons of the conductor, which end up at the right end of the rod. The right end of the rod has an electron deficiency and thus becomes positively charged. In fig. we provide a conducting path to ground (e.g., we can touch

b the conductor). As a result, the electrons escape to the ground. If we remove the path to the ground and the plastic rod, the conductor remains positively charged. Note 1 : The induced charge on the conductor has the opposite sign of the charge on the rod. Note 2 : The plastic rod can be used repeatedly.

Fig. a

Connection to ground

- - -

Fig. b

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