1 From Last Time… Total internal reflection Object Image Lenses and imaging

2 This Friday’s guest lecture Biological Diffraction Prof. Katrina Forest, Bacteriology Friday 8:50 am, 2103 Chamberlin X-ray diffraction Real-space structure

3 Chapter 25: 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~ m  Negative electrons orbit around the nucleus r~ m Example: Lithium 3 protons in nucleus, 3 electrons orbiting

4 + and - charges can be separated Triboelectric  Charge is transferred as a result of mechanical (frictional) action Conduction  charge transfer by contact (spark)

5 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

6 Electric Charges units 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 C Electron: q = -e Proton: q = +e

7 Charge by conduction (touching) Neutral metal Positively charged rod (too few electrons) Less positively charged rod Positively charged metal electron flow

8 Measuring charge Transfer charge to electroscope. Everything equally charge. Like charges on leaves repel. Positive charged rod results in positive leaves

9 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

10 Interactions between charges attractive force between positive and negative charges. repulsive force between two positive or two negative charges Why did the electrons flow?

11 Forces between charges Like charges repel Opposite charges attract All of this without touching — a ‘noncontact’ force Attraction, repulsion decreases with distance

12 Induced charge Charging by induction requires no contact with the object inducing the charge neutral metallic sphere Bring negative charge close. Electrons on sphere move away from rod. charged rubber rod

13 Quick quiz What is the force between these two objects? A. Attractive B. Repulsive C. Zero

14 Lightning doorbell Ben Franklin’s ‘door bell’. Announced presence of lightning so knew to go out and do his experiments!

15 Electrical machines Can mechanize the rubbing process to continually separate charge. This charge can then be transferred to other objects.

16 Quick Quiz A charged rod is brought close to an initially uncharged electroscope without touching The leaves A. move apart B. only one moves away C. move closer together D. depends on sign of rod E. do nothing Positive charged rod results in positive leaves. This is an induced dipole

17 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 The force is a conservative force Electrical forces obey Newton’s Third Law: F 21 = -F 12

18 Quick Quiz Two charges are arranged as shown. What is the direction of the force on the the positively charged ‘test’ particle? + + A B C D E

19 Magnitude of force: Coulomb’s Law Electrical force between two stationary charged particles The SI unit of charge is the coulomb (C ), µC = C 1 C corresponds to 6.24 x electrons or protons k e = Coulomb constant ≈ 9 x 10 9 N. m 2 /C 2 = 1/(4π  o )   o  permittivity of free space = x C 2 / N. m 2 Gravitational force: F G =GM 1 M 2 / r 2 G=6.7x Nm 2 /kg 2

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)Zero Quick Quiz

21 The electric dipole Dipole moment Vector Points from - charge to + charge Has magnitude qs Can all be approximated by electric dipole. Two opposite charges magnitude q separated by distance s

22 Force on an electric dipole What is the direction of the force on the electric dipole from the positive point charge? + A.Up B.Down C.Left D.Right E.Force is zero How does the magnitude of the force depend on ?

23 Induced dipoles (charge redistribution) Bring negative charge close. Electrons on sphere move away from rod. charged rubber rod

24 Induced dipole in insulators A process similar to induction can take place in insulators The charges within the molecules of the material are rearranged

25 The idea of electric fields EM wave made up of oscillating electric and magnetic fields. But what is an electric field? Electric field is a way to describe the force on a charged particle due to other charges around it. Force = charge  electric field The direction of the force is the direction of the electric field.

26 Electric field of a point charge + + Force on this charge… …due to this charge Q1Q1 Q2Q2

27 Question Which vector best represents the electric field at the red dot? A B C D E - A B C - D E