1. Electric & Magnetic Fields
James Clerk Maxwell
(1831–1879)
Electric and magnetic fields manifest their existence through interactions with matter.
Maxwell’s Equations
Differential Form
Integral Form
Lorentz Force
Maxwell's equations are a set of four partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These in turn underlie the present radio-, television-, phone-, and information-technologies.
Conceptually, Maxwell's equations describe how electric charges and electric currents act as sources for the electric and magnetic fields. Further, it describes how a time varying electric field generates a time varying magnetic field and vice versa. Of the four equations, two of them, Gauss's law and Gauss's law for magnetism, describe how the fields emanate from charges.
The other two equations describe how the fields 'circulate' around their respective sources; the magnetic field 'circulates' around electric currents and time varying electric field in Ampère's law with Maxwell's correction, while the electric field 'circulates' around time varying magnetic fields in Faraday's law.
Gauss’ Law
Sometimes called Gauss’ Law of Magnetism
Faraday’s Law
Ampere-Maxwell’s Law
Maxwell’s equation: charges & currents are origins of fields. But charges & current in fields experience forces.
Div form: given electric field and want to know the charge distributions
Integral form: given charge want to know the field

2. Lecture 1 Electric Charges & Coulomb’s Law

3. Electric Charge
Electric charge is an intrinsic characteristic of the fundamental particles that make up objects. +
Positive Charge
Negative Charge
Intrinsic: accompanies those particles wherever they exist.
Positive & negative charges often occur in equal amounts.
Balance: contains no net charge to interact with other objects.
Net charge that can interact with other objects.
Imbalances are small compared to the total amounts of positive and negative charges contained in the object.
Electrically neutral: object contains equal amounts of positive and negative charges
Net charge: imbalance in charge

4. Electric Charge Net charge of a system:
algebraic sum of all the charges
Intrinsic: accompanies those particles wherever they exist.
Positive & negative charges often occur in equal amounts.
Balance: contains no net charge to interact with other objects.
Net charge that can interact with other objects.
Imbalances are small compared to the total amounts of positive and negative charges contained in the object.
Neutral: Electrons are bound to their atoms and cannot move from place to place.
Law: Conservation of charge
The net charge of a closed system never changes

5. Electric Charge $ = n Electric charge is quantized Elementary charge:
Quantized means only discrete values. “Electrical Fluid” is not continuous but is made up of multiples of a certain elementary charge.
Elementary charge:
e = (63) x 10–19 C
Coulomb (C): one coulomb is the amount of charge that is transferred through the cross section of a wire in 1 second when there is a current of 1 ampere in the wire.

6. Charge of Particles Electron Positron Proton Anti-Proton Neutron
Photon
Up Quark
Down Quark
Particles are substances and charge is one of there properties.
Z is the atomic number = number of protons
Neutral atom has equal number of electronics and protons
Nucleus charge= +Ze, atom with Z electrons is neutral.
A quark (pronounced /ˈkwɔrk/ or /ˈkwɑrk/) is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei.[1] Due to a phenomenon known as color confinement, quarks are never found in isolation; they can only be found within hadrons.[2][3] For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves.There are six types of quarks, known as flavors: up, down, charm, strange, top, and bottom.[4] Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay: the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas charm, strange, top, and bottom quarks can only be produced in high energy collisions (such as those involving cosmic rays and in particle accelerators).Quarks have various intrinsic properties, including electric charge, color charge, spin, and mass. Quarks are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge. For every quark flavor there is a corresponding type of antiparticle, known as antiquark, that differs from the quark only in that some of its properties have equal magnitude but opposite sign.The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964.[5] Quarks were introduced as parts of an ordering scheme for hadrons, and there was little evidence for their physical existence until deep inelastic scattering experiments at SLAC in 1968.[6][7] All six flavors of quark have since been observed in accelerator experiments; the top quark, first observed at Fermilab in 1995, was the last to be discovered.[5]
Iron: 26 protons and 30 neutrons
Size of an electron: probably a point object
Nucleus:
~104 times smaller than electron cloud, ~104 times heavier than electron.
Example: nucleus of the iron atom
Size: ~10–15 m, mass: ~10-25 kg
Electron does not orbit nucleus
Electron is described by a wave function
Only know probability of finding an electron at a given location
Nucleus charge= +Ze, atom with Z electrons is neutral.
Proton charge: |e+ | = 1.60 x 10–19 C
Electron charge: |e- | = 1.60 x 10–19 C

7. Interaction of Charges
Charged objects interact by exerting forces on one another.
DEMO: Rod & Fur
Rub a rod with a cloth. Tiny amounts of charges are transferred from one to the other, slightly upsetting the electrical neutrality of each. (Some say it is the organics that are most easily broken by friction. Rods are suspended from threads so electrically insulated from surroundings.
Glass-Silk: glass loses neqative charges and then is unbakanced positively charged
Plastic-Fur: Plastic gains a small unbalanced negative charge.

8. Conductors versus Insulators
Conductors: material in which electric charges can move around “freely.
Insulators: material in which electric charges are “frozen” in place.
Semi-conductor: material in which electric charges can move around but not as freely as in conductors.
Super-conductor: no resistance to the movement of charge.
Properties of conductors & insulators are due to the structure & electrical nature of atoms. Atoms consist of protons, neutrons & electrons. Protons and neutrons are packed tightly in the nucrleus and the electrons orbit the nucleus. Charge of electron and proton have the same magnitude but different signs.
Neutral atoms contain equal amounts of protons and electrons. The electrons are held near the nucleus because they have the opposite electrical sign of the protons & they are attracted to the nucleus. Electrons are bound to their atoms & cannot move from place to place.
Conductors: metals, tap water, human body…..Atoms in a conductor allow one or more of their outermost electrons to become detached. These conduction electrons can move freely throughout the conductor…leaving behind positively charged atoms (positive ions).
Insulators: Air, glass , plastic
Semi-conductors: silicon, germanium
When charge moves an electric current exists. Most materials (even good conductors) tend to resist flow of charge.
Super-conductors: Resistance is zero.

9. Interaction of Charges: Insulators
Force of Repulsion
Force of Attraction
Charged Insulator because charges do not move.
Two charged rods. One is suspended from a thread to electrically isolate it from the surroundings so the charge cannot change. Bring second rod near the haning rod.
We shall put this rule into quantitative form as Coulomb’s Law of Electro-Static Force.
Electrostatic ….relative to each other, the charges are either stationary or moving very slowly.
Plus & minus are arbitrary and was chosen by Benjamin Franklin.
Charges with the same electrical sign repel each other
Charges with opposite electrical signs attract each other.

10. Mobility of Charge
Conductors: material in which electric charges can move around “freely.”
Negatively charged plastic rod will attract either end of the electrically isolated copper rod
Reason: charges in copper rod can redistribute themselves.
Conduction electrons in the closer end are repelled by the negative charge on the plastic rod & move to the far end…leaving it depleted of electrons…thus having an unbalanced positive charge. Positive charge is attracted to negative charge. Although the rod is neutral, it is said to have an induced charge. Positive and negative charges separate because of the presence of a nearby charge.
Positive ions are fixed. Objects can only become positive if negative charge is removed.

11. 3. Break connection to ground, keeping the
Charging by Induction
Bring a charged rod close to conductor.
3. Break connection to ground, keeping the
charged rod in place
Maximizes distance between same charges.
The free charge on the single conducting sphere is polarized by the positively charged rod which attracts negative charges on the sphere. When the conductor is grounded by connecting a wire to the Earth, electrons from the ground neutralize the positive charge on the far face. The conductor is then negatively charged. The negative charge remains if the connection to ground is broken before the rod is removed. After the rod is removed, the sphere has a uniform negative charge.
2. Ground the conductor.
4. Remove the rod. The sphere is charged.

12. Interaction of Charges: Insulators
Insulators: material in which electric charges are “frozen” in place.
Charged Insulator because charges do not move.
Two charged rods. One is suspended from a thread to electrically isolate it from the surroundings so the charge cannot change. Bring second rod near the haning rod.
We shall put this rule into quantitative form as Coulomb’s Law of Electro-Static Force.
Electrostatic ….relative to each other, the charges are either stationary or moving very slowly.
Plus & minus are arbitrary and was chosen by Benjamin Franklin.

13. Conductors versus Insulators
Demo 5A-04: Charges are more readily transferred by conductors
A pair of ping-pong balls is coated with conductive paint & suspended by long, light conductive rods from a metal plate. The plate support is insulating. When both are connected to the generator (negative lead) the balls repel. When on insulating wires, they repel less. Then put on the conducting wired balls but charge one and ground the other & the balls attract.

14. Mobility of Charge Demo: Pie Tins
Pie tins: the pie tins fly off because the sphere is negatively charged and the negative ions in the pie tin want to move as far away as possible from the sphere because of the force of repulsion.

15. Charge Induction Demo: Chimes Charged Conducting thread Grounded
Chimes: The hanging bells are charged (by Van de Graf or Wimshurst machine). The small balls hang from insulating thread. The hanging bells are hung from conducting thread. The central bell is grounded. The hanging ball is attracted to the hanging bell by charge induction causing the bell to strike the bell. The ball picks up charge of the bell and is then repelled, causing it to strike the central grounded bell. The ball is discharged and the process begins all over again.
Charge Leyden jar. Disconnect lead from top of van de graf machine & touch to chimes. The chimes will start to ring. Shows, Leyden jaris charged.
Grounded
Insulating thread

16. Coulomb’s Law of Electro-static Force
Charles-Augustin de Coulomb
( ) q1 q2 r
The electro-static force of attraction/repulsion has a magnitude:
Coulomb’s Law
where:
and the permittivity constant is

17. Coulomb’s Law of Electro-static Force
Force repulsive 1 + 2 r
F12
Force attractive + - 2 r
F12 1
The force exerted by one point charge on another acts along line joining the charges.
•The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs.
F is negative if opposite the r-axis. So, the repulsive force on charge 1 would be (in this case) would be negative
Tipler convention of subscripting forces is as follows: F12 means the force exerted by 1 on 2
Force by “1” on “2”
*Each particle exerts a force of this magnitude on the other particle.
*The two forces form an action-reaction pair.

18. Coulomb’s Law of Electro-static Force
Force exerted by q1 on q2 at a distance r12
q1, q2 in coulombs (C)
r12 in meters (m)
F12 in newtons (N)

19. Problem Solving Strategies:
Draw a clear FORCE diagram
Use consistent units (meter, Coulomb, Newton)
Remember that the force is a vector
Look for (possible) symmetry

20. Quiz 1.
Two charges q = + 1 µC and Q = +10 µC are placed near each other as shown below. Which diagram best depicts the electrostatic forces acting on the charges?
+10 µC
+1 µC A B C

21. Quiz
The nucleus of a Helium atom has a charge equal to twice the proton’s charge. Let FN denote the magnitude of the force the Helium nucleus exerts on one of the electrons in a Helium atom, and Fe denote the magnitude of the force one electron in the Helium atom exerts on the Helium nucleus. Which of the following statements concerning the magnitudes of FN and Fe is true?
(A) FN < Fe
(B) FN = Fe
(C) FN > Fe

22. Quiz
Consider the two cases shown below. In both cases, a central charge q has two charges of equal magnitude at equal distances above and below it. In Case 1, the signs of the two outer charges are opposite, and in Case 2 they are both positive. You are not told the sign of the charge in the center.
In which Case is the magnitude of the net force on the center charge bigger:
Case 1
Case 2
They are the same.
The answer depends on the sign of the charge q in the center. +Q +Q q q -Q +Q
Case 1
Case 2

23. Principle of Superposition
When several point charges are put together, the total force on any one charge is the vector sum of the each of the separate forces acting on that charge.
Exercise: Q2
Determine force on Q1
Q1=Q2=Q3=1C Q3
R=1m
600 Q1 y x F
Another parallel between gravitational force and electro-static force is that superposition also applies to the electro-static forces.
F21
F31

24. Coulomb’s Law Analogous to Newton’s Equation of Gravitation
* k electro-static constant
* Inverse Square Law
* Charge
*Attractive/repulsive depending on sign of charges
*Two kinds of charges
*Dominates on small scale
* G gravitational constant
* Inverse Square Law
* Mass
*Always attractive
*One kind of mass
*Dominates on large scales
DIFFERS

25. Electro-Static Force versus Newton’s Force of Gravitational Attraction
Given such strong electrical interactions, atoms tend to remain uncharged. Matter prefers to be neutral.
Forces we experience, if not gravitational, are electrical in nature (even though the net charge may be zero).
Fel between the proton and the electron in a hydrogen atom in the ground state. From the Bohr model r=0.53 x m.
At the atomic level, one may typically ignore gravity

26. Electro-Static Force versus Newton’s Force of Gravitational Attraction
DEMO: 2 x 4
At the atomic level, one may typically ignore gravity