From Last Time…

Lenses and image formation

Object

Image

qp

Optical Instruments

2

Exam 1 Tue. Sep. 29, 5:30-7 pm, 145 Birge

Covers Chap. 21.5-7, 22, 23.1-4, 23.7, 24.1-5, 26 + lecture, lab, discussion, HW

Study ideas: Exam 1 Practice problems at Mastering Physics Sample exams on website (blank & solutions) Group/Quiz (blank & solutions). Review lab question sheets.

Students with scheduled class conflicts: stay after lecture today to arrange time

8 1/2 x 11 handwritten note sheet (both sides) allowed

Chapter 26: Electric Charges and forces

• Two different kinds of electric charges Benjamin Franklin called these positive, negative

• Negative charges are electrons• Positive charges are protons

• Often bound in atoms: Positive protons in

central nucleus r~10-15 m

Negative electrons orbit around the nucleus r~10-10 m

Example: Lithium 3 protons in nucleus,3 electrons orbiting

+ and - charges can be separated

• Triboelectric Charge is transferred as a result of

mechanical (frictional) action

• Conduction charge transfer by contact (spark)

Separating charge

Charge is conserved. Can be moved around, but not created or destroyed.

•Rubber / fur: electrons transferred to rod

• Rubber has negative charge

•Glass / silk: electrons taken from plastic

• Plastic has positive charge

Electric Chargesunits and quantization

• The SI unit of charge is Coulomb (C )• The electric charge, q, is said to be quantized

quantized = it is some integer multiple of a fundamental amount of charge e

q = Ne• N is an integer• e is the magnitude of charge of electron

= +1.6 x 10-19 C• Electron: q = -e• Proton: q = +e

Charge by conduction (touching)

Neutral metal

+ + + + + + ++ + + + ++

+++

+- --

-

-

Positively charged rod (too few electrons)

+ + + + + + +

Less positively charged rod

+

+++

+

Positively charged metal

+ + + + + + ++ + + + +

+

+++

+- --

-

-

electron flow

Measuring charge

• Touch charged rod to electroscope.

• Charge transferred from rod to electroscope.

• Everything positively charged.

• Like charges on leaves repel.

Positive charged

rod results in positive

leaves.

+ +++

Charge motion and materials

• Insulators (e.g. plastic, wood, paper) electrons bound to atoms, do not move around Even extra charge is stuck Extra charge cannot move around on insulator

• Metals (e.g. copper, aluminum) Some electrons free, positive ions stuck in place Additional charge free to move, distributes over surface

• Ionic solutions (e.g. saltwater) Like conductor, but both positive, negative ions free to move

Forces between chargesLike charges repelUnlike charges attractAll of this without touching — a ‘noncontact’ force

Attraction, repulsion decreases with distance

Induced charge

• Charging by induction requires no contact with the object inducing the charge

neutral metallic sphereElectrons (-) free to move

Bring negative charge close. Electrons on sphere move away from rod.

charged rubber rod

Quick quiz

What is the sense of the force between these two objects?

A. Attractive

B. Repulsive

C. Zero

Lightning doorbell

• Ben Franklin’s ‘door bell’.

• Announced presence of lightning so knew to go out and do his experiments!

++ +

+ ++ +

+---

-

Quick Quiz A charged rod is brought close to

an initially uncharged electroscope without touching

The leaves

A. move apartB. only one moves awayC. move closer togetherD. depends on sign of rodE. do nothing

Positive charged

rod results in positive

leaves.

This is an induced dipole

Vector Nature of Electric Force

a)The force is repulsive if charges are of like sign

b)The force is attractive if charges are of opposite sign

Multiple forces add as vectors.

Electrical forces obey Newton’s Third Law:

F21 = -F12

Quick Quiz

Two charges are arranged as shown. What is the direction of the force on the the positively charged ‘test’ particle?

+

+A

BC

D

E

Magnitude of force: Coulomb’s Law

• Electrical force between two stationary charged particles

• The SI unit of charge is the coulomb (C ), µC = 10-6 C

• 1 C corresponds to 6.24 x 1018 electrons or protons

• ke = Coulomb constant ≈ 9 x 109 N.m2/C2 = 1/(4πo) o permittivity of free space = 8.854 x 10-12 C2 / N.m2

Gravitational force: FG=GM1M2/ r2

G=6.7x10-11 Nm2/kg2

+ --

Equal but opposite charges are connected by a rigid insulating rod.

They are placed near a negative charge as shown. What is the net force on the two connected charges?

A) Left

B) Right

C) Up

D) Down

E) Zero221

rqkq

F =

Quick Quiz

The electric dipole

Dipole moment

Vector

Points from - charge to + charge

Has magnitude qs

€

rp

• Can all be approximated by electric dipole.

• Two opposite charges magnitude q separated by distance s

Force on an electric dipole• What is the direction of the force on the electric

dipole from the positive point charge?

€

rp

+

A. Up

B. Down

C. Left

D. Right

E. Force is zero

How does the magnitude of the force depend on ?

€

rp

Induced dipoles (charge redistribution)

Bring negative charge close. Electrons on sphere move away from rod.

charged rubber rod

Induced dipole in insulators

• A process similar to induction can take place in insulators

• The charges within the molecules of the material are rearranged