ELECTROSTATICS 3. P.Ravindran, PHY041: Electricity & Magnetism 15 January 2013: Electrostatics 3

Transcription

1 ELECTROSTATICS 3 q 0

2 Electro negativity ti it Rl Relative electro negativity ranking for some common materials from electron donating materials (+, glass) to electron accepting materials (, teflon) Glass Human Hair Nylon Silk Fur Aluminum Paper Cotton Copper Rubber PVC Teflon

3 Where do charges come from? Rubbing materials does NOT create electric charges. It just transfers electrons from one material to the other. When a balloon rubs apiece of wool... electrons are pulled from the + wool to the balloon The balloon has more electrons than usual. wool + The balloon: charged, The wool: +charged

4 Law of Conservation of Charge Conservation of Charge An object that has unequal numbers of electrons and protons is electrically charged. An atom with a net positive charge is a positive ion; it has lost one or more electrons. An atom with a net negative charge is a negative ion; it has gained one or more electrons. Law of Conservation of Electric Charge During any process, the net electric charge of an isolated system remains constant ( is conserved). Ttl Total charge bf before= Ttl Total charge after. The principle that electrons are neither created nor destroyed but are simply transferred from one material to another is known as conservation of charge. 4

5 Electrostatics: Electrical charges at rest Law of Electrostatics: Like charges repel, Unlike charges attract Conductors: Free electrons allow conduction of charge e metal

6 Conductors Conductors: materials that allow electrons to flow through them easily. Conductors CANNOT be easily charged by friction as the extra electrons gained can easily escape.

7 Insulators (non Conductors): Tightly bound electrons do not conduct charge readily wood No electron transfer! Semi Conductors: Silicon and Carbon, among others that fall in between good conductor and good insulators. Often used in computer chips and other electronics.

8 Insulators Insulators: materials that do NOT allow electrons to flow through them easily. Insulators can be easily charged by friction as the extra electrons gained CANNOT easily escape.

9 Induction: The production of a charge in an uncharged body by bringing a charged object close to it. When negatively charged rod is put near a metal can... induced charges attraction electrons of fthe can are pushed hd away from the rod. top of the can: positive bottom of the can: negative metal can repulsion & attraction > repulsion

10 Grounding What is grounding? g An object is grounded when it is connected to the earth through a connecting wire. If a charged conductor is grounded, it will become neutral.

11 Grounding b How does grounding occur? When we touch a metal ball of positive charge... + electrons flow from the earth to the metal ball to neutralize the metal ball. Metal ball becomes neutral.

12 Grounding How does grounding occur? Similarly, if the metal ball is of negative charge... extra electrons flow from the metal ball to the earth and the ball becomes neutral.

13

14 Lightning kills more than 60 people p and injures more than 400 people a year in the US one mile every five seconds about 20,000 C Voltage of up to x volts

15

16 Electroscope: An electroscope is a device used to detect electrostatic charge on an object.

17 Charge is determined by the surplus or deficiency of electrons in relation to protons and is measured in coloumbs (C) 1 C = 6.25 X electrons This is a lot of charge most charges are measured in microcoloumbs (µc) 1 µc = 10 6 C Coloumb s Law: k = 9 X 10 9 N m 2 /C 2 this value is for charges separated by air F = kq 1 Q 2 r 2 Coloumb s Law: Electric Charge (Q) exerts a force that depends directly on the charges and inversely on the square of the dsa distance cebetween ee the charges!

18 An electrostatic charge of 60.0 µc exerts a force of 175 N on a charge of 50.0 µc. How far apart are the charges? Q 1 = 60.0 µc Q 2 = 50.0 µc F = 175 N r = kq 1Q 2 F r =? = (9 x 10 9 N m 2 /C 2 )(60.0 x 10-6 C)(50.0 x 10-6 C) 175 N =.391 m

19 Example Why is Coulomb s force a central force? Solution: Coulomb s force between two charges always acts Coulomb s force between two charges always acts along the line joining them and hence, it is a central force.

20 Answer Me!!! Why will a balloon stick to the wall?

21 Static Electricity Static Electricity is created by the build up of electrons on an object s surface.

22 A balloon has a negative charge when rubbed by woollen cloth. 2 During rubbing, what have been transferred between the woollen cloth and the balloon? A Electrons B Protons C Neutrons

23 A balloon has a negative charge when rubbed by woollen cloth. 2 During rubbing, what have been transferred between the woollen cloth and the balloon? A Electrons B Protons C Neutrons

24 Sub Atomic Particles PROTON NEUTRON ELECTRON CHARGE Positive (+1e) None (0) Negative (-1e) MASS 1 AMU 1 AMU 1/1836 AMU 1 elementary charge (e) ()is x C One coulomb (C) is 6.25 x elementary charges. Electric charge of an object can not be broken down smaller than one elementary charge.

25 Practice Problem 1 An object can NOT have a charge of 3.2 x C 4.5 x C 80x C 9.6 x C

26 Answer Problem 1 An object can NOT have a charge of 3.2 x C 4.5 x C 80x C 9.6 x C

27 Practice Problem 2 A metal sphere having an excess of +5 elementary charges has a net electric charge of 32x C 4.5 x C 8.0 x C 9.6 x C

28 Practice Problem 2 A metal sphere having an excess of +5 elementary charges has a net electric charge of 32x C 4.5 x C 8.0 x C 9.6 x C

29 Practice Problem 3 Fill in the diagram to represent the charge distribution on the neutral spheres when a positively charged rod is brought near sphere X. X Y Z

30 Practice Problem 3 Fill in the diagram to represent the charge distribution on the neutral spheres when a positively charged rod is brought near sphere X. X Y Z

31 Conductors in Electrostatic Equilibrium

32 Gauss s Law surface E da q in 0 Permittivity of free space: ε = x 10 C 2 / (N m 2 ) k 910 x Nm / C 4 0 q in EdA cos surface 0

33 Insulators vs Conductors In an insulator, excess charge is not free to move. In conductors the electrons are free to move.

34 Electrostatic Equilibrium of Conductors Electrostatic Equilibrium for a conductor no net motion of charge within a conductor. Most conductors, on their own, are in electrostatic equilibrium. Ex: in a piece of metal sitting by itself, there is no current.

35 Characteristics of Conductors in Equilibrium 1. The E field is zero at all points inside a conductor (regardless if it is hollow or solid). 2. If an isolated conductor carries excess charge, the excess charge resides on its surface. 3. The E field just outside a charged conductor is perpendicular to the surface and has magnitude σ/ε 0, where σ is the surface charge density at that point. 4. On an irregularly shaped conductors the surface charge density is biggest where the conductor is most sharp.

36 If the conductor is placed in an electric field at first there is a movement of electrons(current) but eventually the movement stops and their is equilibrium. If the E was not zero inside the conductor the movement would continue and there would not be equilibrium.

37 Solved Example A charge q is placed at the midpoint of the line joining two identical charges Q. What should be the value of q if this system of three charges is to be in equilibrium? Solution: Q q Q 2 x For equilibrium, 1 Qq 1 QQ Q 0 q x 4 (2x) 4 0 0

38 Note: Inside the cylinder there are no electric field lines.

39 Ex 1: Point charge Inside a Spherical Metal Shell A 5.0μC charge is located as shown in Fig a). If the shell is electrically neutral, what are the induced charges on its inner and outer surfaces? Are those charges uniformly distributed? Whatisthe the E field pattern?

40 Ex 1: Solution Strategy Since the shell is electrically neutral, E=0 inside the shell. Take a Gaussian surface inside the shell. This Gaussian surface must encompass an enclosed charge of zero because E=0 inside the conductor. The point charge is 5μC so since the net charge is zero: 5μC+ x =0 x= 5μC. This x is the charge on the inside surface of the shell. Since the shell is neutral the outside surface of the shell must have a charge of x= 5μC

41 Ex 1: Solution Strategy cont d Since the point charge is not in the center of the spherical shell llbut off centered, there will be more positive charges closer to the point charge. The charge distribution in the inner wall of the shell will be more dense closer to the point charge. The field lines between the point charge and the shell will be closer together nearest to the point charge. However, in the outer surface of the shell the negative charges will be evenly distributed. This is the case no matter where inside the shell, the point charge is located. The field lines are shown in figure b) E lines are always perpendicular p to the conductor surface.

42 Hollow Conductors Charge placed INSIDE induces balancing charge ON INSIDE q

43 Hollow Conductor A charge placed OUTSIDE induces charge separation ON OUTSIDE surface. +q E=0 + +

44 Problem: A square plate of copper with 50.0 cm sides has no net charge and isplaced in a region of uniform electric field of 80.0 kn/c directed perpendicularly to the plate. Find (a) the charge density of each face of the plate and (b) the total t charge on each face. a ) E N / C C / Nm C m b) Q A C/ m m Q C

45 Give the dissimilarities between Coulomb s force and force of gravitation. Solution: Coulomb s force (i) Force between charges (ii) Repulsive or attractive (iii) Not active over large distance (iv) Affected by the medium between the charges Force of gravitation Force between masses Always attractive Active over very large distance Unaffected by the medium between the bodies

46 Electric field (intro.) A charge creates a physical condition in the space surrounding itself called the electric field such that, any other charge present in that space experience electric force. No boundary, but strength considerably decreases away from the charge responsible for that. Intensity of field at a point Force on unit positive charge placed at that point. A vector represented by E SI unit: N C 1 At a point, where strength of the filed is E, a charge q experiences a force of magnitude F = q E

47 Solved Example If an oil drop of weight 3.2 x N is balanced in an electric field of 5 x 10 5 N C 1, then find the charge on the oil drop. Solution: W = N, E = N C 1 W = q E W E q= = 19 = C 5

48 Applying Gauss Law Spherical Symmetry Electric field due a charged sphere of charge q and radius R (i) Field at an outside point, i.e., r > R q ˆ Gaussian surface E n S E.ds = ε 0 2 q 1 q E 4 r = E = ε 4 2 r 0 0 Note that E is same at all points on the Gaussian surface The field is the same as if the whole charge is placed at the centre of the shell

49 (ii) At a point on the surface, r = R 1 q E= 4 ε R 0 2 (iii) At a point inside the spherical shell r < R Gaussian surface No charge is enclosed by the Gaussian surface. E.ds 0 E 0 S

50 + r + + q r q E= for r R 4 ε 2 r + E=0, for r<r 0 Variation of electric field intensity from the centre of the shell with distance

51 Solved Example The uniform surface charge density on a spherical copper shell is What is the electric field strength on the surface of the shell? Solution: The electric field on the surface of a uniformly charged spherical conductor is given by, E= 1 q 4 ε 2 0 R o

52 Solved Example A spherical charged conductor has a uniform surface charge density. The electric field on its surface is E. If the radius of the sphere is doubled keeping the surface density of charge unchanged, what will be the electric field on the surface of the new sphere? Solution: The electric field on the surface of a uniformly charged spherical conductor is given by, 2 1 q 4 R E = 4 ε 2 R 2 4 R 0 0 o Thus, E is independent of the radius of the sphere. As is constant, E remains the same.

53 Solved Example The uniform surface density of a spherical conductor is and the electric field on its surface is E 1. The uniform surface density of an infinite cylindrical conductor is 2 and the electric field on its surface is E 2. Is the expression correct? E E Solution: The electric field on the surface of a charged spherical conductor is given by, 1 E 1 o E o (i)

54 Solution Contd. The electric field on the surface of a charged cylinderisgiven is by, E 2 q 2 2 r o o ( r = radius and = length ) E o (ii) From equations () (i) and () (ii) we get, E E

55 Solved Example A spherical shell of radius 10 cm has a charge C distributed uniformly over its surface. Find the electric field (a) Inside the shell; (b) Just outside the shell; (c) At a point 15 cm away from the centre Solution: q = C, R = 0.1 m, r = 0.15 m (a) Inside the shell, electric field is zero q 2 10 (b) E = = ε R = NC q 2 10 (c) E' = = ε r =8 10 NC

56 Electric potential Electric potential at a point the work done in bringing unit positive charge from infinity to that point against the electric forces. W V= q SI unit Volt (V) 1J 1V= 1C One volt the electric potential at a point if one joule of work is done in bringing gunit positive charge from infinity to that point.

57 Solved Example If a positive charge be moved against the electric field, then what will happen to the energy of the system? Solution: If a positive charge be moved against the electric field, then energy will be used from an outside source.

58 Solved Example If 80 J of work is required to transfer 4 C charge from infinity to a point, find the potential at that point Solution: W =80 J, q = 4 C, V =? W 80 V= = =20V Q 4