physics 122: introduction to electricity and magnetismdmw/phy122/lectures/lect_01b.pdf · 2019. 9....

28 August 2019 Physics 122, Fall 2019 1

Physics 122: introduction to electricity and magnetism

In which we learn to use the second natural force, which

❑ holds matter together;

❑ is the source of the most easily-detected form of radiation;

❑ is the foundation of much of modern technology, certainly the parts worth the most money.

http://www.flickr.com/photos/stefnisson/sets/

Our aims in teaching Physics 122

❑ To help you understand the physical basis of electromagnetism.

❑ To teach you how to solve problems involving forces, fields and energies created by electric charges and currents.

❑ To teach you how to solve more complex sorts of physics problems than you could hitherto, by using more of the vector algebra and integral calculus you have been learning along the way.


Human features of Physics 122

One professor:

❑ Me (Dan Watson), lecturing M-W-F, 12-12:50 PM

Seven workshop teaching assistants:

❑ Olayinka Akinyemi, Alaina Attanasio, Carter Ball, Trung Ha, Quinn Kaufman, Ethan Savitch, and Peter Tomlinson

staffing a total of (currently) 14 workshops.

Plus a larger corps of laboratory TAs, whom we share with PHY 142 and PHY 122P.


Printed and electronic features of Physics 122

❑ One textbook: Halliday, Resnick, and Walker, Fundamentals of Physics, tenth edition.

❑ Computer-projected lectures, for greater ease of presentation of diagrams, math, and animations, and for online accessibility on our…

❑ Web site: www.pas.rochester.edu/~dmw/phy122,in which you can find, among many other things,

• Complete lecture notes

• Homework answers and solutions

• Practice exams

• Exam solutions

The website is not up yet, but will be before Friday’s lecture.


http://www.pas.rochester.edu/~dmw/phy122

Onerous features of Physics 122

All assignments are the same for the two lecture sections:

❑ Frequent homework, usually due weekly. Worth 15% of your grade.

❑ Two midterm exams – worth 20% each – and a comprehensive final exam worth 30% of your grade, given during common exam times.

❑ Workshop participation, worth 5% of your grade.

❑ Laboratory reports, worth 10% of your grade.

But we will assign final grades on a straight scale, not “on the curve.”

❑ This is to your advantage. There is no limit to the supply of good grades!


http://goatmilk.files.wordpress.com/2008/05/darth-vader-face1.jpg

Mid-lecture Break

❑ Please review the syllabus and ask questions about anything we have left unclear about the course and its requirements.

❑ Workshops start next week. First homework due the week after that.

Boston Museum of Science


http://www.mos.org/sln/toe/history.html

Today in Physics 122: electric charge and the electrostatic force

❑ Electric charge, force and Coulomb’s law

❑ What is charge?

❑ How to solve electrostatic force problems with point charges.


Adam Block, KPNO

http://www.noao.edu/kpno/kpno.html

Electric charge and electrostatic force

Generation of charge and electric force was known at least as early as about 600 BC (Thales).

❑ That the force can act across a vacuum was shown in the late 1600s (Boyle).

❑ That there are two different types of charge that neutralize each other was realized in the mid 1700s (du Fay, Franklin).

❑ By then some (e.g. Priestley) suspected the force is inverse-square, like gravity.


Primitive voltage generator: amber and fur. Rub them together and the amber will thenceforth make the fur stand up when close by.

Charge : electrostatic force : : mass : gravity

Not every piece of matter responds to electrostatic forces.

❑ Electric charge is that property of matter which determines how strongly that particular bit of matter responds to the presence of other charges.

❑ In that sense it plays the same role that mass does, in the gravitational force.

❑ But unlike mass, charge comes in two different types: like types exert repulsive forces on each other, and unlike types exert attractive forces on each other.

❑ Benjamin Franklin was the first to assign algebraic signs (+,-) to the charge types, which we still use as he did.

• In fur-and-amber generation, he decided to call the fur’s charge positive, the amber’s negative.


Charge conservation

Franklin was also the first to show that electric charge is conserved (1747): that the total electric charge on a closed system never changes. (Like mass, energy, momentum…)

❑ He did this by demonstrating the persistence of charge collected in a good insulating jar.

❑ Nowadays the most precise and accurate demonstrations of charge conservation are sensitive searches with high-energy particle accelerators for particle decays that could happen if charge were not conserved. For example, in neutrons (n), protons (p), electrons (e) and neutrinos ():


n p e → + +

→p + +

The second of these decays, which would violate charge conservation, has never been seen to happen; the first one happens at least 1026 times as often as the second.

Coulomb’s Law

In 1785 Charles de Coulomb demonstrated experimentally that the force between two fixed (non-changing) electric charges of value Q1 and Q2 varies with varying distance very accurately according to an inverse-square relation:

where k is a constant.


1 21 2 1 22

1 2

ˆQ Q

k→ →

→

=F rr

1Q 2Q

1 2→r 1 2ˆ→r

1 2→F

As most physics books, bold letters indicate vectors. Bold letters with hats indicate unit vectors.

2 0.0000000000000001.

Modern value:

Choose the correct statement.

is the force charge 1 exerts on charge 2. Of course if we know this force, we also know it’s given by …


1 2→F

2 1 :→F

2 1 1 2

2 1 1 2

2 1 1 2

2 1 1 2

A. , according to Newton's second law.

B. , according to Newton's second law.

C. , according to Newton's third law.

D. , according to Newton's third law.

→ →

→ →

→ →

→ →

=

= −

=

= −

F F

F F

F F

F F

2 1 1 2

2 1 1 2

2 1 1 2

2 1 1 2

A. , according to Newton's second law.

B. , according to Newton's second law.

C. , according to Newton's third law.

D. , according to Newton's third law.

→ →

→ →

→ →

→ →

=

= −

=

= −

F F

F F

F F

F F

Coulomb’s law (continued)

Coulomb’s experiment involved an accurate force measurement, using a torsional balance, between two small, charged metal spheres. He adjusted the distance between the spheres and measured the force with the balance.

❑ Coulomb probably invented this sort of balance, which has been used ever since in measurement of very small forces.


Coulomb’s experimental appa-ratus (Wikimedia Commons).

//upload.wikimedia.org/wikipedia/commons/0/04/Bcoulomb.png

http://en.wikipedia.org/wiki/File:Bcoulomb.png

Units for electric charge

In magnitude,

❑ The MKS unit of electric charge is the coulomb. (abbreviated coul or C) Thus the units of the constant k have to be

and its value is measured to be

❑ For reasons to be made clearer later this semester, we usually define another constant to use in place of k:


21 2F kQ Q r=

2 2

2 2

coul NmN

m coulk k= =

9 2 -29.0 10 Nm coul .k =

212

0 20

1 coul8.85 10 .

4 Nmk

−= = Permittivity of vacuum (free space)

What is electric charge?

1. Is charge a continuous, fluid-like property of matter, in the sense that it can be made as small as one wants?

2. Is charge completely independent of other properties of matter, something that can be “poured into” matter, as Franklin (among others) thought?

These questions were hotly debated in the 1700s-1800s, at about the same time that the final arguments took place about whether matter it self was made of continuous fluid or “atoms.” The answers are

1. No

2. No


What is electric charge? (continued)

So what is it, then?

Charge turns out to be an intrinsic property of the subatomic constituents of matter, the elementary particles.

❑ There is a smallest finite amount that electric charge comes in. This was theorized to be true in the mid-1800s (by Faraday) and finally demonstrated experimentally in 1909 by Millikan and Fletcher.

❑ The magnitude of that smallest amount, called the quantum of electric charge or elementary charge, is

That is to say, one coulomb is a lot of charge.

More on the elementary particles and charge in PHY 123.


191.6022 10 coul.e −=

What is electric charge? (continued)

As you’re no doubt aware, ordinary matter is made of atoms, which in turn are made of protons, neutrons and electrons.

❑ Atoms in their stable states contain equal numbers of electrons and protons.

❑ The charges of the electron and proton are likely to be exactly equal and opposite: the electron has –e and the proton +e, following Franklin’s definition.

• Experimentally,

(Bressi et al. 2011).

❑ So ordinary matter is electrically neutral, to very high precision.


21electron proton

neutron

0 10Q Q e

Q

−+ =

=

http://adsabs.harvard.edu/abs/2011PhRvA..83e2101B

“Triboelectricity”

Rubbing amber and fur together results in a charge on both. The sign of the charge on the amber is negative.

Explain physically what must be going on in this process, which is called triboelectricity.

Electrons live in the outer parts of atoms, so there are electrons present where the rubbing occurs.

Evidently the material fur is made of holds onto electrons less tightly than that which amber is made of. The rubbing results in the transfer of electrons from fur to amber.


Electrostatic forces

Upshot from the homework and exam perspective: we now have a new force, the electrostatic force, to treat in mechanics problem by use of Newton’s laws.

❑ And it will work a lot like gravity, since it’s inverse-square.

❑ Good news: you already have mastered how to do such problems, in PHY 121.

❑ Bad news: you now have to remember how to do such problems.

• So shake the rust off by looking at the example electrostatic force-balance problems in the textbook (pp. 563-567), and the different one which follows.


Example: three charges

Three electric charges, Q, Q, and –Q, are arranged as shown. Find a formula for the force on –Q.

❑ What kind of problem is this, and what tools do we need?

• Coulomb’s Law, an appropriate coordinate system, and trigonometry to add the vectors.


Q−

Q

Q

6d

5d

5d

Three charges (continued)


❑ What is the appropriate coordinate system in which to decompose the force vectors and then add the results?

• Any coordinate system will do, of course, but it’s easiest to choose one which fits the symmetry of the problem.

Q−

Q

Q 6d

5d5d

4d

x

y

3d 3d

1F 2F

1 2

2

225

Qk

d

=

= −

F F



Q−

Q

Qx

y

❑ What are all the x-y components on our test charge –Q?

So the x componentscancel.

2 2

1 2 2

2

2 12

3cos

525 25

cos25

x

x x

kQ kQF

d d

kQF F

d

= − = −

= = −

1xF 2xF



Q−

Q

Qx

y

2 2

1 2 2

2 1

2

1 2 2

2

2

4sin

525 25

So add them up for the final answer:

8

125

8That is: magnitude ,

125

toward the midpoint

of .

y

y y

y y y

kQ kQF

d dF F

kQF F F

d

kQ

d

Q Q

= − = −

=

= + = −

−

1yF

2yF

physics 122: introduction to electricity and magnetismdmw/phy122/lectures/lect_01b.pdf · 2019. 9....

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