30 August 2012 Physics 122, Fall 2012 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 most lucrative parts.

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.

30 August 2012 Physics 122, Fall 2012 2

Human features of Physics 122

Two professors: Me (Dan Watson) – lecturing T-R, 2-3:15 PM Regina Demina – lecturing M-W-F,

12-12:50 PM Six workshop teaching assistants: Dev Ashish Khaitan (head TA), Jennafer Banister, Alex

Breindel, Eric Garcell, Chris Mullarkey, Ryan Waldman Nine laboratory teaching assistants: Dan Lum (head TA), Yiting Duh, Shihhan Hung, Sam

Knarr, Erini Lambrides, Catherine Polyakov, Austin Taylor, Jeff Vankerkhove, Kaming Woo

You’ll have one of each. 30 August 2012 Physics 122, Fall 2012 3

Human features of Physics 122 (continued)

The professors cover the same material in their lectures, but differ in lecturing style; will differ somewhat in

emphasis of certain topics owing to their differences in research interests. • Prof. Demina: elementary

particle physics, the smallest scales of nature.

• Prof. Watson: astrophysics, the largest scales of nature.

30 August 2012 Physics 122, Fall 2012 4

Printed and electronic features of Physics 122

One textbook: Douglas Giancoli, Physics for scientists and engineers, fourth edition, v. 2.

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/~regina/PHY122, in which you can find, among many other things, • Both sets of lecture notes • Homework answers and solutions • Exam solutions

30 August 2012 Physics 122, Fall 2012 5

Onerous features of Physics 122

All assignments are the same for the two lecture sections: Frequent homework, 11 problem sets in all; usually due

weekly. Worth 5% of your grade. Two midterm exams – worth 20% each – and a

comprehensive final exam worth 40% 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! 30 August 2012 Physics 122, Fall 2012 6

Mid-lecture Break

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

If you are adding the course, feel free to use permission code 7937.

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

Boston Museum of Science

30 August 2012 Physics 122, Fall 2012 7

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.

30 August 2012 Physics 122, Fall 2012 8

Adam Block, KPNO

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.

30 August 2012 Physics 122, Fall 2012 9

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.

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. 30 August 2012 Physics 122, Fall 2012 10

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 (ν):

30 August 2012 Physics 122, Fall 2012 11

n p e ν→ + +

→p ν ν+ +

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.

30 August 2012 Physics 122, Fall 2012 12

1 21 2 1 22

1 2

ˆQ Qk→ →→

=F rr

1Q 2Q

1 2→r 1 2ˆ →r

1 2→FAs in the book, 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 …

30 August 2012 Physics 122, Fall 2012 13

1 2→F2 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 FF FF FF 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 FF FF FF 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.

30 August 2012 Physics 122, Fall 2012 14

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

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:

30 August 2012 Physics 122, Fall 2012 15

21 2F kQ Q r=

[ ] [ ]2 2

2 2coul NmNm coul

k k= ⇒ =

9 2 -29.0 10 Nm coul .k = ×

212

0 20

1 coul8.85 10 .4 Nm

k επε

−= ⇒ = ×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

30 August 2012 Physics 122, Fall 2012 16

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. 30 August 2012 Physics 122, Fall 2012 17

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.

30 August 2012 Physics 122, Fall 2012 18

21electron proton

neutron

0 10Q Q e

Q

−+ = ±

=

“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.

30 August 2012 Physics 122, Fall 2012 19

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.

30 August 2012 Physics 122, Fall 2012 20

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.

30 August 2012 Physics 122, Fall 2012 21

Q−

Q

Q

6d

5d

5d

Three charges (continued)

30 August 2012 Physics 122, Fall 2012 22

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

5d 5d4d

x

y

3d 3d

1F 2F

1 22

225Qk

d

=

= −

F F

Three charges (continued)

30 August 2012 Physics 122, Fall 2012 23

Q−

Q

Q x

y

θ θ

What are all the x-y components on our test charge –Q? So the x components cancel.

2 2

1 2 2

2

2 12

3cos525 25

cos25

x

x x

kQ kQFd d

kQF Fd

θ

θ

= − = −

= = − 1xF 2xF

Three charges (continued)

30 August 2012 Physics 122, Fall 2012 24

Q−

Q

Q x

y

θ θ

2 2

1 2 2

2 1

2

1 2 2

2

2

4sin525 25

So add them up for the final answer:

8125

8That is: magnitude ,125

toward the midpoint of .

y

y y

y y y

kQ kQFd d

F F

kQF F Fd

kQd

Q Q

θ= − = −

=

= + = −

−

1yF

2yF