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Electricity Greeks learned about charge by rubbing amber (fossilized tree resin) Greek word for amber = “elektronPicture from wikipedia

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Page 1: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

ElectricityGreeks learned about charge by rubbing amber (fossilized tree resin)

Greek word for amber = “elektron”

Picturefrom

wikipedia

Page 2: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Atomic Structure - A Who’s Who

J. J. Thomson1856-1940

Ernest Rutherford1871-1937

Robert Millikan1868-1953

Discovered electron(Measured charge divided by mass)

Discovered nuclearstructure

Measured charge ofelectron (thereby finding its mass)

Page 3: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Benjamin Franklin 1706-1790

Charles-Augustinde Coulomb1736-1806

Henry Cavendish1731-1810

Defined positive vs.negative charge

Discoveredelectricforce law

Page 4: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Michael Faraday

1791-1867

• Left school at age 13• became book binder • read books he bound• learned science (but not math!)• asked author he read to work in his lab• became great scientist and inventor

• invented notion of “fields”

Page 5: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Karl Gauss 1777-1855

Numerous contributionsto electromagnetic theory

Page 6: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Alessandro Volta1745-1827

Invented battery

Page 7: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Otto von Guericke1602-1686

http://www.hp-gramatke.net/history/english/page4000.htm

Credited with first electrostatic generator - Put ball (made of sulphur) on wooden cradle, spin it and rub by hand

Page 8: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Ewald Jürgen von Kleist1700-1748

Pieter van Musschenbroek1692-1761

Independently developedthe “Leyden jar,” an early capacitor (1745)

Page 9: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Alessandro Volta1745-1827

Invented battery - “Voltaic pile”

Page 10: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Batteries - from Volta to today

Cathode

Anode

Page 11: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

André-Marie Ampère1775-1836

Page 12: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Georg Ohm1789-1854

Page 13: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Gustav Kirchhoff1824-1887

Contributed to:Electric CircuitsSpectroscopyBlack-body radiation

Page 14: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

John Ambrose Fleming1849-1945

Vacuum tubediode

Russell Ohl1898-1987

Diodes with “p-n junctions”- Toward modern electronics!

Page 15: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Transistors (1940s-50s, 50s-60s, and today)Lee De Forest

1873-1961Triode

Page 16: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

Modern transistors - npn and pnp

junctions

Integrated circuits -

William Shockley1910-1989

John Bardeen1908-1991

Walter Brattain1902-1987

Page 17: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

William Gilbert1544-1603

Said Earth is magnet with

iron core

Page 18: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Hans Christian Oersted1777-1851

Discovered thatmagnetism can be created by currents

Page 19: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Nikola Tesla1856-1943

Scientist and inventor, AC power, AC motors, wireless transmission

Page 20: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Hendrik Lorentz1853-1928

Worked on electricity, optics, relativity

Page 21: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Joseph Larmor1857-1942

Page 22: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Wilhelm Weber1804-1891

Invented the telegraph(with Gauss)

Karl Gauss 1777-1855

Numerous contributionsto electromagnetic theory

Page 23: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Edwin Hall1855-1938

Discovered effect while graduate student at

Johns Hopkins

Page 24: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Jean-Baptiste Biot1774-1862

Felix Savart1791-1841

Developed law in 1820

Page 25: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Electricity

André-Marie Ampère1775-1836

Page 26: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Michael Faraday

1791-1867

Joseph Henry 1797-1878

electromagnets, First Secretary of the

Smithsonian

Page 27: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Luigi Galvani 1737-1798

early studies in bioelectricity,

colleague of Volta

Page 28: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

Heinrich Lenz1804-1865

Page 29: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Magnetism

James Clerk Maxwell1831-1879

one of the greatest physicists of all time, electromagnetism, thermodynamics/

statistical mechanics

Page 30: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

Heinrich Hertz1857-1895

Page 31: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

John Poynting1852-1914

Page 32: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

Willebrord Snellius

1580-1626

Rene Decartes1596-1650

Thomas Harriot

1560-1621

ibn Sahl ~940-1000

Page 33: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

Christiaan Huygens1629-1695

Page 34: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

Arthur Compton1892-1962

Page 35: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Who’s Who in Optics

Lord Rayleigh(John William Strutt)

1842-1919

Page 36: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lectures forUniversity Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Chapter 21

Electric Charge and Electric Field

Announcements

Page 37: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Forces of NatureAll interactions in the entire universe (!) can be described by four forces

You’ve studied only the “gravitational”force

This semester, we’ll do “electricity and magnetism”

Amazingly the two turn out to be part of the same force - the “electromagnetic” force

We’ll hint at a third force soon, the last one is covered in Modern Physics class

Supermassive black hole at the center of the Milky Way (Sagittarius A)

Page 38: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Review of the Gravitational ForceObjects have an intrinsic property called “mass”

An object’s mass can be 0 (light - a photon)Two objects with mass attract each other, the force is

This works for any two objects: “Universal gravitation” is a vector force along line connecting masses - sign force is attractive (always!)

is a measure of strength of gravitational force (“coupling constant”)

is small gravity is very weak

Force goes like weaker for masses that are further apart

Force proportional to mass more mass means stronger force

F = −Gm1m2

r2r̂

⇒⇒

⇒G

G

⇒1/r2 ⇒

F (r̂)

m

Page 39: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric ChargeObjects have another intrinsic property called “charge”

Greeks learned this by rubbing amber (fossilized tree resin)

Greek word for amber = “elektron”

q

Do “Balloons” Demo

Amber from wikipedia

Page 40: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric ChargeTwo kinds of charges

Called positive (+) and negative (-)By convention (due to Benjamin Franklin)

Objects with charge feel a forceLike charges repel, opposites attract

This is known from experiment/observation

Objects can also be charge neutralMost matter is net charge neutral

Neutral matter contains the same amount of positive and negative charges

Why is most matter neutral?

Benjamin Franklin

1706-1790

Page 41: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Matter as ChargesMatter is made up of protons, neutrons and electrons

The unit of charge is Coulombs:

The charge of a proton is

Note,

Memorize this!

q = e

q = 0

q = −e

[q] = Coulombs

e = 1.60217653(14)× 10−19Ce � 1.6× 10−19C

melectron � mprotonmelectron

mproton� 1

1836

Page 42: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Make-up of AtomsSince ,they behave very differently!

When the charges are “free,”electrons move much easier than protons

They feel the same force(Newton’s Third Law pairs),but their acceleration is different!

Inside atoms, we think of the lighter electrons “orbiting” protons like the Earth orbits the Sun

This will change when we learn quantum mechanics (Modern Physics)

Protons and neutrons reside in the nucleus of the atom

melectron � mproton

Fe on p Fp on e

motion

Page 43: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

How Do We Know?Electrons discovered in 1897 by Thomson

It was thought that the positive chargeswere distributed evenly throughout the matter (Thomson’s “plum pudding” model)

Rutherford experiment 1907His assistant (Geiger) developed a counter of alpha particlesAlpha particles (helium nuclei, discovered in 1895) shot into a foil made of gold, they found more particles bounced backwards than expected

Conclusion - Almost all the mass is localized in small regionsIf an atom was the size of a football stadium, the nucleus would be basketballs at the 50-yard line and the electrons would be in the highest seatsMost of what makes up matter (your desk, your fingers, ...) is almost entirely empty space!

Page 44: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Atoms - Neutrals and Ions

Neutral matter is neutral not because it is made up of uncharged particles, but because it is made up of

equal numbers of positive and negative charges.

Page 45: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

The Electric ForceHow would you determine the electric force between charges?

Same way Cavendish did for gravitation in 1787- torsional balance!Coulomb measured the electrostatic force(for charges at rest) in 1784.

Cavendish already did it, but didn’t publish!

Charles-Augustinde Coulomb1736-1806

Henry Cavendish1731-1810

Page 46: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Coulomb’s Law• The result (Coulomb’s Law) is astounding!

• Looks just like gravitational force!• Again an “inverse square law”• Mass m => Charge q• Gravitational constant G =>

Coulomb’s constant k(electrostatic coupling constant)

• --------

F =kq1q2r2

Finish this

Page 47: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lectures forUniversity Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Chapter 21

Electric Charge and Electric Field

Announcements

Page 48: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Coulomb’s Law• The result (Coulomb’s Law) is astounding!

• Looks just like gravitational force!• Again an “inverse square law”• Mass m => Charge q• Gravitational constant G =>

Coulomb’s constant k(electrostatic coupling constant)

F =kq1q2r2

Measure with voltmeter and plasma ball?

Page 49: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Examples of electrical force calculated—IA fascinating comparison of gravitational force to electrostatic force is shown in Example 21.1 and Figure 21.11.

Regard Problem-Solving Strategy 21.1.

See also Example 21.2 and Figure 21.12.

Page 50: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Examples of electrical force calculated—IIConsider Example 21.3 and Figure 21.13.

See also Example 21.4 and Figure 21.14.

Page 51: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Movement of charges—charging by conduction• Materials that allow

easy passage of charge are called conductors. Materials that resist electronic flow are called insulators. The motion of electrons through conducts and about insulators allows us to observe “opposite charges attract” and “like charges repel.”

Page 52: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electrons move freely and charges may be induced• Take a child’s toy, a rubber balloon. If you rub the balloon

vigorously on a fuzzy sweater then bring the balloon slowly toward a painted concrete or plaster wall, the balloon will stick to the wall and remain for some time. The electrostatic force between static electrons and the induced positive charge in the wall attract more strongly than the weight of the balloon.

Page 53: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Static electricity about an insulator can shift• The motion of static charges about a plastic comb and light bits

of paper can cause attractive forces strong enough to overcomethe weight of the paper.

Page 54: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric fields may be mapped by force on a test charge

If one measured the force on a test charge at all points relative to another charge or charges, an electric field may be mapped.

This experiment is often done in one’s mind (called a “gedanken experiment”).

Page 55: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric fields I—the point chargeFields of force may be sketched for different arrangements of charge.Consider Example 21.6 and Figure 21.19.

Page 56: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric fields II—charges in motion within a fieldConsider Example 21.7.

Consider Example 21.8 and Figure 21.21.

Page 57: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric fields add as vectorsRegard Figure 21.22.

Review Problem-Solving Strategy 21.2.Follow Example 21.9 and Figure 21.23.

Page 58: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

A field around a ring or line of chargeReview Example 21.10 and Figure 21.24.

Review Example 21.11 and Figure 21.25.

Page 59: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

A field around a disk or sheet of chargeReview Example 21.12 and Figure 21.26.

Review Example 21.13 and Figure 21.27.

Page 60: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric field lines map out regions of equivalent force I

Page 61: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Electric dipoles and water• As mentioned

in the introduction, the dipole force of water is vital to chemistry and biology.

Page 62: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

Consider force and torque on a dipole• Regard Figure 21.32.

• Follow Example 21.14 and Figure 21.33.

Page 63: Electricity - Plasma Physics at West Virginia Universityulysses.phys.wvu.edu/~pcassak/Phys112/Slides.pdf · Atomic Structure - A Who’s Who J. J. Thomson ... the last one is covered

The electric field of a dipole revisited

Consider Example 21.15.

Figure 21.34 illustrates the example.