Ch. 15 Electric Force and Electric Field. Concept questions #2, 4, 7, 9 Problems #1, 3, 4, 10, 11, 12, 15, 19, 21, 25, 27, 29, 38, 40, 42, 50

Transcription

1 Ch. 15 Electric Force and Electric Field Concept questions #2, 4, 7, 9 Problems #1, 3, 4, 10, 11, 12, 15, 19, 21, 25, 27, 29, 38, 40, 42, 50

2 Primary goal of physics class. Study how the universe works Learn how the laws of nature affect us How to take advantage of these laws.

3 Physics 1, studied mechanics and thermodynamics Physics 2, study properties of electricity, magnetism and their properties. Will also look at waves, sound optics, and will see how these are related to each other and electricity and magnetism

4 Electricity is used almost everywhere Understanding and using electricity may be the most important finding by man since fire. Without electricity, there would be no computers, phones, television, radio, microwaves We would revert back to the 19 th century.

5 In chapter 15 we will cover the electric charge and electric force and then study electric fields. Chapter 16 cover electric energy. Later we will discuss circuits, which are an application of other chapters.

6 Ch. 15 Electric charge physical observable that allows a material to have electrical properties. Easy way to see evidence of charge is to rub 2 nonconductors together. After doing so, you can exert a force on another nonconductor.

7 Simple experiments can show that there are two types of charge. Benjamin Franklin named them positive and negative. Rub a rubber or plastic rod against some fur. Then rub a glass rod against silk. The two rods will attract each other. Repeat with two rubber or two glass rods and there will be a repulsive force. Franklin s convention was that the charge on the glass is positive. The charge on the rubber is negative. Conclusion Like charges repel, unlike charges attract

8 Atomic description of charge The basic carriers of positive charge are protons, which are located in a nucleus. The nucleus is surrounded by electrons, which carry negative charges. In most matter, there are just as many protons as there are electrons. The net charge is zero. The matter is neutral.

9 In a solid the nucleus of each atom is held in place, so the protons don t move. Electrons are much lighter than protons m p = 1836 m e Electrons are much more easily accelerated by forces. (They have less inertia) Therefore, electrons are more easily transferred from one material to another. Objects become charged by gaining or losing electrons.

10 Charge transfers readily from one object to another when the objects come in contact with each other. Rubbing two materials together increases the contact area and thus makes it easier for electrons to move. This is analogous to water moving down a pipe. The wider the pipe, the easier it was for the water to go through it.

11 Important rules for charges. The total electric charge is a conserved quantity. Neutral objects have an even number of positive and negative charges. Charge is not created When an object is charged, it either gives or takes an electron to another object, therefore changing the charge of the object. When you rub a plastic rod with fur, the rod becomes negatively charged when electrons move from the fur to the rod.

12 Properties of charge In 1909 Robert Millikan discovered the quantization of charge. The charge of an object is always a multiple of some fundamental value that can t be further subdivided. Call this value e. Objects only have charges of integer multiples of e. Can t have a charge of 0.2e or 0.5e.

13 Unit of charge e, the fundamental unit of charge, has a value of: x C (round to 1.6 x C) The SI unit of electric charge is the coulomb (C)

14 Conductors and insulator We used the term nonconductor earlier. The text definition: In a conductor, electric charge moves freely in response to an electric force. All other materials are insulators. An insulator (glass, rubber)is a nonconductor.

15 Conductors Metals are conductors. In a conductor it is easy for the electrons to move around in the material. Since the electrons can move easily, the material conducts charge. The charge can move around the entire surface of the material. Copper is a good conductor. That is why it is commonly chosen for wiring.

16 Insulators When an insulator becomes charged, the charge doesn t move into other regions of the material. The transferred electrons can t move around very far. When I charge up my pen, I can only pick up the pieces of paper with the end that was rubbed with the hair. Since the charges stay locally concentrated, the charge at the end, is strong enough to pick up the paper.

17 Charge by Conduction First you have a negatively charged rod and a neutral insulated conducting sphere. (The sphere is not touching any other conductors.) 1) When the rod is placed near the sphere, a net positive charge moves near the rod, a net negative charge moves to the opposite side. 2) Upon contact, electrons from the rod move onto the sphere and neutralize the positive charges. 3) Taking away the rod, the sphere is left with a negative net charge.

18 Charge by Conduction The sphere now has a negative charge. The sphere still has the same amount of protons, but now there are more electrons. The object being charged by conduction will be left with the same type of charge as the object doing the charging. We can repeat this with a positively charged rod.

19 Charge by Induction Using conduction, the two materials came in contact with each other. Charging by induction does not require physical contact. Idea of being grounded. Any object connected to a conductor that is buried in the Earth is grounded. The Earth can accept or supply an unlimited amount of electrons.

20 Charge by Induction First you have a negatively charged rod and a neutral insulated conducting sphere. When the rod is brought near the sphere, the charges separate out.(as in the first step in conduction) Now the grounding wire is attached to the sphere. The repulsive force from the negatively charged rod will push some of the electrons off the sphere and down the wire. After removing the wire, the sphere has an excess of positive charges.

21 Charge by Induction The sphere will still have the same number of protons (positive charges) but now has a smaller amount of electrons (negative charges). The sphere has an induced positive charge. Also the negatively charged rod didn t lose any of its charge, because it never came in contact with the sphere. When charging by induction, the charged object (sphere) obtains a charge opposite of the charge of the charging object (rod).

22 Electric Force Properties of the electric force exerted between two stationary particles 1) directed along a line joining the two particles and is inversely proportional to the square of the distance separating the particles ( 1/r 2 ) 2) proportional to the product of the magnitudes of the charges of the particles. 3) It is attractive if the charges have opposite signs. Repulsive if the charges have the same signs.

23 Electric Force and Coulomb s Law Coulomb s law mathematically describes the force between the two charges. q1 q2 F k 2 r k (Coulomb constant) = 9x10 9 N m 2 /C 2 This applies to point charges and to spherical distributions, where r is the separation of the two centers of charge.

24 Important values Charge(C) Mass (kg) Electron -1.6x x10-31 Proton 1.6x x10-27 Neutron x C of charge requires about 6.3x10 18 protons or electrons. 1 C is a lot of charge. You would typically deal with magnitudes of charges around 10-6 C.

25 Electric Force Remember that force is a vector quantity. All forces obey Newton s 3 rd Law of equal and opposite reactions. Even if two charges have different magnitudes, they exert equal and opposite forces on each other.

26 Example of electric force Find the force the two protons separated by 10-9 meters exert on each other. Is the force attractive or repulsive. F k (1.6 x10 19 C)(1.6 x m 2 19 C) 2.3x10 10 N The force is repulsive.

27 Superposition principle What to do when there are more than 2 charges. When more than 1 charges act on the charge of interest, you need to compute the force from each charge individually and then add up the forces using vectors.

28 The Electric Field The electric force behaves much like the gravitational force, in that it can act through space. The two charges don t have to be in contact. These are examples of field forces. An electric field is produced by a charged object and surrounds the object. The field then exerts a force on any other charged object.

29 Electric Field The electric field that is produced by a charge Q at the location of a test charge q 0 is efined as the force exerted by Q on q 0, divided by the test charge q 0. E = F/q 0 SI units of electric field are N/C Electric field is a vector

30 Electric Field The Force exerted by an electric field depends on the field strength (E) and the charge (q) that the field is exerted on. F = qe Lets look at the force that Q exerts on q F = k Qq/r 2 The magnitude of the electric field the Q produces at q is E = k Q/r 2

31 Electric Field The magnitude of the electric field produced by a single charge is: E k Electric field is a vector. The direction will be from the location of the charge to the point where the field is being measured. q r The superposition principle is used here if more than one charge is present. Need to add up the individual electric fields from each charge. 2

32 Direction of Electric Field The electric field acts along what are called field lines. For a point charge, the electric field lines will spread out in a radial direction from the charge. If the charge is positive, the field lines radiate outward. If the charge is negative, they radiate inward.

33 Electric Field Lines The electric field vector, E, is always tangent to the field lines at each point. The number of lines per unit area, through a perpendicular surface is proportional to the field strength. If the lines are close together, the field is strong.

34 Field Lines Field lines begin on positive charges and end on negative charges. Some lines will begin or end infinitely far away. The number of lines leaving a positive charge or ending at a negative charge is proportional to the magnitude of the charge. Field lines can never cross each other. see examples on pg 510,511.

35 Conductors in Electrostatic Equilibrium Electrostatic Equilibrium occurs when there is no net motion of charge. Properties of isolated conductor 1 The electric field is zero everywhere inside the conducting material 2 All excess charge is on the surface 3 The electric field just outside the conductor is perpendicular to the surface 4 Charge accumulates at sharp points, where the surface is most sharply curved.

36 Will talk about Van de Graaf generator at end of chapter. Electric Flux and Gauss s Law Gauss s law is a second technique for calculating electric fields, that when applied to situations where there are specific symmetries, is much more efficient than Coulomb s law. Will introduce the concept of electric flux.

37 Electric Flux When electric field lines pass through a given surface, we say there is flux through the surface. For example, if the field lines are tangent to the surface, they don t penetrate at all and there is no flux.

38 Electric Flux Take a uniform electric field passing through a surface of area A. The surface A is perpendicular to the field lines. The number of field lines per area is related to the strength of the field. E N/A, where N is the number of lines. N EA, so the number of field lines is proportional to the product of the field strength times the area. This product is the electric flux ( e) e =EA

39 Flux e = E A This works when the electric field has a constant magnitude over the area and the field lines are normal to the surface. If the surface is slanted the flux becomes: e = E A cos Only the component of the electric field that passes through the surface produces any flux.

40 When using Gauss s law we will make use of a Gaussian surface which is an imaginary surface that located where we want to calculate the electric field. To use Gauss s Law the electric field must be constant on all points of a surface. example: a point charge

41 Gauss s Law applied to a point charge e = E A The electric field from a point charge is E = k Q/r 2 Surround the point charge with a Gaussian sphere of radius r. e = E A = (k Q/r 2 )(4 r 2 )=4 k Q relate the Coulomb constant to the permittivity of free space ( 0 ) 0= 1/(4 k) = 8.85x10-12 C 2 /(N m 2 ) e = Q/ 0

42 The flux through the surface is equal to the charge the surface surrounds divided by 0. This can be proven, via calculus, to work for any closed surface. Gauss s Law relates the flux though a closed surface to the charge the surface encloses. e = Q enc / 0

43 Flux when describing flux though through the boundary of a closed surface, lines that enter the enclosed volume have negative flux lines that exit the enclosed volume produce positive flux. the sign of the net flux indicates whether the enclosed charge is positive or negative.

44 Gauss s law is very useful when there is a charge distribution that has a high degree of symmetry. Otherwise, producing a Gaussian surface where the electric field is uniform is not practical. useful for point charges, spheres, long cylinders and line charges, or planes. Need to pick a Gaussian surface that has all points equidistant from the charge

45 Using Gauss s law to find the electric field of a point charge. Use Gaussian sphere. e = E A = E (4 r 2 ) and e = Q/ 0 setting the two definitions of flux equal to each other, we get E (4 r 2 ) = Q/ 0 Q E = or E = k Q/r 2 4 r o 2 This was the same expression we found using Coulomb s law earlier.

46 Look at a line of charge Suppose you have a cable with a charge Q and a length L. We can use Gauss s Law to find the electric field a distance r from the cable. we assume the cable is very long to negate the end effects. Our Gaussian surface is going to be a cylinder whose axis is located on the cable. e = E A = E (2 rl) = Q/ o Q E = 2 The field strength is proportional to 1/r L (quite often we will call Q/L the linear charge density ) 0 r

47 Infinite sheet of charge need the sheet of charge to be infinite to neglect the edge effects. Let the sheet have a surface charge density: = charge/area = Q/A or Q = A For a plane the Gaussian surface needs sides that are perpendicular and parallel to the plane. A box or upright cylinder will do. e = E A and e = Q/ o the is flux coming out/in through both ends of the Gaussian box

48 e = E A = E (2A) = Q/ o E = Q/(2A o ) remember = charge/area = Q/A E = /(2 o ) Note that the electric field is constant. If you have an infinite sheet of charge, the electric field would have a constant magnitude wherever you measured.

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