Study Guide #2. L. Colonna-Romano/T. Keil. Electricity and Magnetism

Transcription

1 PH1120 Electricity and Magnetism L. Colonna-Romano/T. Keil Term B99 Study Guide #2 With this Study Guide, we will discuss work and energy in situations involving an electric field and related concepts. We will also look at devices, called capacitors, that store energy in an electric field and see how they behave when placed in simple circuits. Objective 4 Electric Potential Energy 1) Calculate the work one must do against electrical forces in moving a point charge between two points in a uniform electric field. 2) Calculate the work one must do against electrical forces in moving a point charge between two points in the vicinity of another point charge. 3) Calculate the work one must do in assembling a given arrangement of two or more point charges. Suggested Study Procedures for Obj. 4 Study Sec and The textbook describes the work done by the electric force. The work that you do against the electric force is just the negative of this. Study carefully Example Note that this example applies the principle of conservation of energy in a similar manner as that done in mechanics when there are no nonconservative forces doing work. Study Example Suggested Problems for Obj. 4 1) Exercises: 24-1, 24-5, Objective 5 Electric Potential Define electric potential. Calculate the potential difference between two points in a uniform electric field. Calculate the absolute potential which exists at a specified location in space due to: a) a stationary point charge, given its value and location, and b) two or more stationary point charges, given their respective values and locations. 1) Calculate the potential difference between two points, given the value of a charge and the work involved in transporting it between two points. 2) Determine the motion of a charged particle accelerated through a known potential difference in a uniform electric field. 3) Apply conservation of energy (kinetic and electrical potential) to problems involving charged particles moving in electrostatic fields.

2 PH1120B99 Study Guide #2 2 Suggested Study Procedures for Obj. 5 Study Sec Young and Freedman define potential in terms of a point charge. They then describe potential difference (a physical quantity used frequently) by Eq There is an alternate approach that may be easier to understand. The potential difference can be defined as the work that you do against electric forces in moving a positive charge from point a to point b divided by q. W a b (by you) = V b V a q Study the four examples, 24-3 through 24-5 and Suggested Problems for Obj. 5 1) Exercises: 24-11, 24-13, 24-17, 24-25, 24-27, ) Problem: 24-54, Objective 6 Potential and the Electric Field Given an electric field configuration, be able to construct equipotential lines and given a configuration of equipotential lines, be able to construct electric field lines associated with the equipotentials. Suggested Study Procedures for Obj. 6 Study Sec Note how this section and Examples 24-9 and relate directly to your first lab. 1) Exercise: Suggested Problems for Obj. 6 Objective 7 Capacitance 1) Define capacitance. 2) Given a set of capacitors in a series-parallel configuration, connected to a voltage source: a) calculate the equivalent capacitance of the set; b) explain how charge is distributed among the capacitors, and how the potential changes across each capacitor; c) calculate the charge stored on each and the potential drop across each capacitor. Suggested Study Procedures for Obj. 7 Study Sec through 25-3 paying particular attention to Examples 25-1, 25-2, 25-5 and 25-6.

3 PH1120B99 Study Guide #2 3 Suggested Problems for Obj. 7 1) Exercises: 25-1, 25-9, 25-11, 25-14, ) Problem: Objective 8 Capacitors and the Energy of the Electric Field 1) Calculate the electrostatic energy stored on a charged capacitor. 2) Calculate the final electrostatic energy in capacitors which have been initially independently charged and then connected together. 3) Calculate the energy density in an electric field. Suggested Study Procedures for Obj. 8 Study Sec The derivation leading to Equation 25-9 is important. Make sure that you can do problems similar to Example Suggested Problems for Obj. 8 1) Exercise: ) Problems: 25-44, Homework Homework Assignment #5 due Wednesday, November 10, 1999 Prob The electric field between two square copper plates is 200 N ; the plates C are 1.00 cm thick and 1.30 m on a side. They are separated by a distance of 2.00 cm. a) Neglecting edge effects, what is the charge on each plate? b) If a proton is released from rest at the surface of the positively charged plate, what will its velocity be when it strikes the negatively charged plate? What will be its kinetic energy? c) Repeat this calculation for an electron released from the negatively charged plate. d) Comment on the result of parts b) and c). Prob Three charges are assembled at the corners of an isosceles triangle as shown in Fig. 1. The long edges of the triangle are of length 1.00mandtheshortedgeis0.600 m. If q 1 =3.00 µc andq 2 = q 3 =2.00 µc, answer the following questions. 1) Calculate the work you must do to assemble the three charges at the corners of the isosceles triangle as shown in the figure. 2) Calculate the work you must do to bring a charge of 1.00 µc from very far away to the point midway between q 2 and q 3. 3) Suppose the 1.00 µc charge is now released from that point. Decide whether or not it would move and, if so, in which direction will it move. Justify your answer.

4 PH1120B99 Study Guide #2 4 q 1 q 2 q 3 Fig. 1. Prob. 5-2 Prob An α-particle consists of two protons and two neutrons; it is the same as a helium nucleus and has a charge of twice that of a proton and a mass of kg. In a nuclear physics experiment, α-particles are accelerated to a high velocity and then strike a gold target. The gold nucleus has a charge of 79 times the charge of a proton; the electrons that move around the gold nucleus can be ignored. What must the velocity of the α-particles be (very far from the target) if, in a head-on collision with a gold nucleus, the center of an α-particle reaches a distance of m from the center of a gold nucleus. The gold atom is bound in a large crystal and does not move. Homework Assignment #6 due Friday, November 12, 1999 Prob A positive charge of magnitude Cisplaced1.00 cm above the origin of a coordinate system, and a negative charge of the same magnitude is placed 1.00cm below the origin, both on the z-axis. What is the potential energy of a positive charge of magnitude C placed at the position (x, y, z) =(10.0cm, 0, 15.0 cm). Repeat the problem assuming that the positive charge is placed at (10.00 cm, 0, 0). Prob A point charge of +3 e, wheree is the magnitude of the charge on the electron, is positioned at the origin and a second charge of 2 e is positioned on the x-axis at x = a. a) Sketch the potential function V (x) versusx for all x. b)atwhatpoint(orpoints)isv (x) zero? c) How much work is needed to bring a third charge of +e to the point x = a 2 on the x-axis? Prob Two large parallel metal sheets carrying equal and opposite electric charges are separated by a distance of 45.0 mm. The electric field between them is uniform and has magnitude 600 N. a) What is the potential difference between the sheets? b) Which sheet C is at the higher potential, the one with positive charge or the one with negative charge? c) What is the surface charge density σ on the positive sheet?

5 PH1120B99 Study Guide #2 5 Homework Assignment #7 due Monday, November 15, 1999 Prob The plates of a parallel-plate capacitor are 4.70 mm apart, and each plate carries a charge of magnitude C. The plates are separated by vacuum. The electric field between the plates has a magnitude of V m. a) What is the potential difference between the plates? b) What is the area of each plate? c) What is the capacitance? d) What is the surface charge density on the negatively-charged plate? Prob See Fig on p. 793 in your text. Assume C 1 =2.50 µf, C 2 =5.00 µf, C 3 = 6.00 µf and an applied potential V ab of 50.0 V. Calculate a) the charge on each capacitor, b) the potential difference across each capacitor, c) the potential difference between points a and d. Prob An 18.0 µf capacitor is charged to a potential difference of 800 V. The terminals of the charged capacitor are then connected to those of an uncharged 10.0 µf capacitor. Compute a) the original charge in the system, b) the final potential difference across each capacitor, c) the energy stored in the system before the capacitors are connected, and d) the energy stored in the system after the capacitors are connected. Where has the lost energy gone? Prob Homework Assignment #8 due Wednesday, November 17, 1999 Exercise on p. 793 in the text. Prob a) How should four 2.0 µf capacitors be connected to have a total capacitance of i) 8.0 µf, ii) 2.0 µf, iii) 1.5 µf, and iv) 0.5 µf. b) A 16.0 pf parallel-plate capacitor is charged by a 10.0 V battery. If each plate of the capacitor has an area of 5.0 cm 2, what is the energy stored in the capacitor? What is the energy density (energy per unit volume) in the electric field of the capacitor if the plates are separated by air? Prob A parallel-plate capacitor has 6.15 J of energy stored in it. The separation between the plates is 1.20 mm. If the separation is decreased to 0.60 mm, what is the energy stored if: a) the capacitor is disconnected from the potential source, so the charge on the plates remains constant? b) the capacitor remains connected to the potential source, so the potential difference between the plates remains constant? LCR sg2.tex 1 Nov :40 p.m.