Ph272- General Physics II (Electricity and Magnetsism)

Lesson 1: Ch. 22 - Coulomb's Law

Key Topics

Overview

• Electromangetic interaction is one of the four known fundamental interactions (forces):

Interaction	"particles"
Gravitional interaction	ALL
Electromagnetic interaction	Charges
Strong nuclear interaction	Nucleons
Weak nuclear interaction	Nucleons

• Relevancy - Electromagnetic interaction accounts for most of the phenomena we encounter in our daily lives.

For example: electric lights, radio signals, magnets, visible light, x-rays, chemical reactions.

Can you think of any other examples?

• Electrostatics vs. Electrodynamics - Electromagnetic interaction is the interaction between charges. The phenomena are quite different when the charges are stationary or accelerated. We will first examine the case of stationary charges (electrostatics). In this lesson, we will examine the law which governs the forces exerted by the charges on each other when they are at rest (Coulomb's Law).

Electric Charges

• Two types of charges - Fact: We know that charges can attract or repel each other therefore there must be (at least) two types of charges. By convention, we call them postive and negative charges.

Fact: Like charges repel and unlike charges attract.

-> Q. What experiment can you perform to decide that there are only two types of charges and not three types or more?

• Charge are quantized - Fact: Evidence shows that the smallest amount of charge is that carried by protons and electrons (*), we say charges are quantized.

Charge of proton = 1.6x10(-19) Coulomb and charge of electron=-1.6x10(-19) Coulomb.

(Analog: money is quantized because the smallest denomination is a penny).

(* Current theory predicts quarks have fractions of the quantized charge but there are no DIRECT experimental evidences)

• Neutral Objects - Macroscopic objects usually contain the same number of protons and electrons, therefore they are neutral.

• Charging an object -

A macroscopic object can be charged by removing or adding electrons (protons are strongly bounded to the nucleus therefore it is not easily removed, if some of the protons are removed then the element changes into a different element).

Charging can be done by rubbing the object, heating, etc.

-> Q. Can you think of other ways of charging?

-> Q. If the charge of an object is +1 Coulomb, how many electrons were removed?

Charging a conductor - The electrons inside a conductor can move freely. If you add some electrons to a conductor, the electrons will spread out evenly (why?)

Charging an insulator - If you can some electrons to a localize region in an insulator, the electrons tend to stay locailzed because they can not move freely in an insulator (they "sticks" to the atoms).

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Coulomb's Law

• The forces exerted on each other by two stationary "point" charges are given by the Coulomb's Law. (Section 18-3, Eq.18-2)
• "Strength" of the Coulomb force:

-> Q.What is the force of repulsion between two +1C charges sperated by 1 meter?

• "Point" Charges - The charges can be treated as "point" charges if their separation is much larger than their diameters.
• Force Vector - The force vector MUST be labelled by two subscripts (because the force is due to the intereaction between two bodies)
• Convetions of this textbook:

F12 denotes force exerted by q1 on q2, and

r12 is the vector pointing from q1 to q2 therefore r12 = r2 - r1.

-> Questions:

With these convetions, draw F12 on Fig, 18-8.

Is the force vector on q1 or q2?

Which way is F12 pointing if both q1 and q2 are both positives or both negatives?

Which way is F12 pointing if both q1 and q2 are one is positive and the other is negative?

Answers the same questions for F21.

• Mathematical technique:
  • Express a vector in Cartesian coordinates
  • Find the magnitude of a vector
  • Find the unit vector corresponding to a direction.

• Qualitative features of Coulomb's Law - Coulomb's Law is expressed in a vector equation (Eq. 18-2).

-> Q. Does this equation contains all the following features?

The magnitude of the force is proportional to the product q1q2 and invesely proportional to the square of separation.

The direction of the forces are repulsive for like charges and attractive for unlike charges

The two forces are equal and opposite: F12 = - F21.

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Superposition Principle

• Statement 1: The total force on q1 exerted by q2 and q3 is the sum the two forces:

F on 1 = F21 + F31

-> To practice, do problem 18.8 and 18.9, P.620. Note: add vectors.

• Statement 2 : A charge of 3 C can be thought of a composite of 2 C and 1 C or 4 C and -1C, etc.

This principle allows us to simplify certain problems, here is an example.

(You have to come to lecture to see this example!)

-> Q. Can you think of other examples?

-> Q. What features of Coulomb's Law which makes Statement 2 vaild?

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Demo:

(1) Wimhurst machine - generates static electricit.

(2) Charging a plastic comb by rubbing against your hair.

Use the comb to pick up pieces of paper.

-> Q. How does it work? The pieces of paper are netural. Isn't the Coulomb force zero?

Review

• Answer review question in text, P.619.
• Write a short review (in your own words) of this lecture

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