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

Transcription

1 PH1120 Electricity and Magnetism L. Colonna-Romano/T. Keil Term B98 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 PH1120B98 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 PH1120B98 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 11, 1998 Prob The electric field between two square copper plates is 100 N ; the plates C are 1.00 cm thick and 1.00 m on a side. They are separated by a distance of 3.00 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? Prob Three charges are assembled at the corners of an isosceles triangle as shown in Fig. 1. The long edges of the traingle are of length 1.00mandtheshortedgeis0.600 m. If q 1 =3.00 µc andq 2 = q 3 =4.00 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 PH1120B98 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 the charge 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, an α-particle just touches the surface of a gold nucleus. The radius of a gold nucleus is m. The gold atom is bound in a large crystal and does not move. Homework Assignment #6 due Friday, November 13, 1998 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 Prob Prob Prob Prob Prob Exercise on p. 762 in the text. Exercise on p. 763 in the text. Homework Assignment #7 due Monnday, November 16, 1998 Exercise 25-2 on p. 792 in the text. Exercise on p. 792 in the text. Exercise on p. 794 in the text. Homework Assignment #8 due Wednesday, November 18, 1998 Exercise on p. 793 in the text.

5 PH1120B98 Study Guide #2 5 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 7.15 J of energy stored in it. The separation between the plates is 1.30 mm. If the separation is decreased to 0.65 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 4 Nov :56 p.m.