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### ASSIGN1

Course: PHYS 2208, Spring 2007
School: Cornell
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______ Name: Section: ______________________________ Assignment 1: Electric Forces and Fields Section Instructor: ______________________________ Concepts: electric charge electric forces electric fields electric field line model electric fields near conductors in electrostatic eq. Coulomb's law conductors and insulators superposition charge in an electric field Reading in text: Chapter 21: Sections 1-6....

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______ Name: Section: ______________________________ Assignment 1: Electric Forces and Fields Section Instructor: ______________________________ Concepts: electric charge electric forces electric fields electric field line model electric fields near conductors in electrostatic eq. Coulomb's law conductors and insulators superposition charge in an electric field Reading in text: Chapter 21: Sections 1-6. Chapter 22: Sections 1-5, 8, 9. Chapter 25: Section 7. Assignment: Solutions posted on Wednesday, January 31. Quiz may be given on or after Tuesday, February 6. D 1. Two positive point charges, each having charge +Q , and two -q +Q negative point charges, each having charge -q , are at the corners of a square of side length D , as shown. (a) Draw a diagram showing the electric forces acting on the D upper left + Q charge. (b) What must be the magnitude of -q (in terms of Q ) in order for each of the + Q charges to be in electrostatic +Q -q equilibrium? (c) Derive an expression for the magnitude of the resulting net electric force acting on the upper right -q charge (in terms of Q , D , pure numbers (like 2, , etc.), and any required physical constants such as the electrostatic constant k ). What is the direction of this force? 2. An electric dipole is shown in the diagram on the last page of this assignment. (a) At each point marked , carefully construct a vector arrow showing the total electric field at that point due to the dipole. Let the lengths of your arrows indicate the relative magnitudes of the field at the various points. [Hints: Start by defining an arrow of a certain convenient length (say, ) to be the electric field due to one of the charges at one unit distance from that charge. Then, at each point , scale the electric field contribution due to each charge by the distance of that point from the charge, according to the inverse-square law. Notice that several points are related by symmetry so you don't have to do as many vector constructions as you might first expect.] (b) In what ways does the pattern of resultant electric field vectors (magnitudes and directions) agree with the pattern of electric field lines for an electric dipole shown in your textbook (Fig. 22-5)? 3. A sphere of charge of radius R has a total charge q distributed uniformly throughout its volume. (a) What is the volume charge density (= charge per unit volume) inside the sphere in terms of q and R ? (b) What is the direction of the electric field outside the sphere if q is positive? 1 Physics 208, Spring 2007 Cornell University (c) What is the magnitude of the electric field outside the sphere a distance r ( r > R ) from the sphere's center? [Hint: Think of the sphere as being composed of a series of concentric shells of charge. What is the electric field at r due to a given shell? If the electric fields at r due to all of the shells are added together, then this (vector) sum should be the total electric field due to the entire sphere (superposition principle).] What (d) is the magnitude of the electric field inside the sphere a distance r ( r < R ) from the sphere's center? (See the hint given in part (c) above.) (e) Sketch a graph of the magnitude of the electric field E () versus r () from r = 0 to r = 3R . 4. A spherical metal shell with inner radius b and outer radius c has a net charge of + Q . (a) Where is this charge located? c (b) Draw electric field lines everywhere there is an electric field. b (c) Write an expression for the component of the electric field just outside the shell's outer surface that is to this surface. (Take the positive direction for this E to be away from the conductor at this surface.) (d) Show that this electric field expression can be written as E = 4 k = 0 where is the surface charge density (= charge per unit area) on the outer conducting surface. (This turns out to be an expression for the electric field just outside the surface of any conductor in an electrostatic situation, regardless of the conductor's shape.) Now a separate point charge -Q is placed at the center of the shell's hollow cavity, electrically insulated from the shell itself. (e) Draw electric field lines everywhere there is an electric field. (f) Mark the location(s) and amount(s) of any separated charge on the shell, including + and - sign(s). (g) Draw a graph of the electric field E r as a function of distance r from the shell's center from r = 0 to r = 3c . Let positve and negative values of E r refer to directions away from and towards the shell's center, respectively. 5. An electron moving horizontally in an L y oscilloscope enters a region between two oppositely charged parallel metal deflecting plates that are L = 4.0 cm long and H = 0.8 cm apart. The electron is deflected upwards (+ y x direction, ) during its passage through this region and emerges at the right with final velocity components v x = 10 10 7 m / s and v y = 2.0 10 6 m / s . . (a) Draw electric field lines showing the electric field produced by charges on the plates. (b) Show the locations and signs of charges on the plates. (c) Carefully draw the shape of the electron's path between the plates and after it leaves this region. (d) How much time does it take the electron to pass through the region between the plates? H Physics 208, Spring 2007 2 Cornell University (e) What are the direction and magnitude of the electron's acceleration while it is between the plates? (f) What is the magnitude of the electric field in the region between the plates? Text questions and problems for study and review: Chapter 21: Questions 1, 3, 4, 5, 6, 7, 9, 10. Problems 1, 4, 5, 9, 11, 20, 29, 48, 59. Chapter 22: Questions 1, 2, 3, 4, 6, 8. Problems 1, 2, 7, 8, 11, 13, 16, 41, 43, 45, 46, 75, 86. Physics 208, Spring 2007 3 Cornell University Section: ______ Section Instructor: ______________________________ Name: _________________________________ Physics 208, Assignment 1 Diagram for Problem 2 +Q -Q
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