Midterm I Review - 9

Announcements MIDTERM I February 9 (1hr. 3:50-4:50 pm,) UA1120 Topics Covered (Chapter 19) Electric charges Coulomb’s Law Gauss’ Law Conductors in electrical equilibrium Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 9 February 5, 2006 Coulomb’s Law Electric Field Point charge Potential at point 2 Point charge at 1 Electric Field at point P Due to distribution of charges Force felt by charge q at P Due to an electric field Potential Difference and Electric Field Using vectors for the electric force is not useful (incomplete or messy). How do we visualize? Field lines give better mapping (related to force via 4 rules). Equipotential lines are perpendicular to field lines and represent scalars. Gauss’s Law allows us to find a relation between electric flux (i.e. field lines), charge and electric field. By using appropriate symmetries, the equation simplifies and allows us to find the electric field or the charge. A conductor in electrostatic equilibrium has the following properties: The electric field is zero everywhere inside the conductor. Any net charge on the conductor resides entirely on its surface. The electric field just outside the conductor is perpendicular to its surface and has a ?/?0 magnitude , where ? is the surface charge density at that point. E= ?/?0 On an irregularly shaped conductor, the surface charge density is greatest where the radius of curvature of the surface is the smallest. These rules plus Gauss’s Law allow us to determine the amount of charge on the surfaces of conductors in electrostatic equilibrium. 17 Two point charges are located on the x axis. The first is a charge +Q at x = –a. The second is an unknown charge located at x = +3a. The net electric field these charges produce at the origin has a magnitude of 2keQ/a2. What are the two possible values of the unknown charge? 18 Three charges are at the corners of an equilateral triangle as shown in the Figure. (a) Calculate the electric field at the position of the 2.00-?C charge due to the 7.00-?C and –4.00-?C charges. (b) Use your answer to part (a) to determine the force on the 2.00-?C charge. 2.00-?C 7.00-?C –4.00-?C 14. A point charge of 12.0 ?C is placed at the center of a spherical shell of radius 22.0 cm. What is the total electric flux through (a) the surface of the shell and (b) any hemispherical surface of the shell? (c) Do the results depend on the radius? Explain. 18. A positive point charge Q is located at the center of a cube of edge L. In addition, six other identical negative point charges q are positioned symmetrically around Q as shown in Figure P24.17. Determine the electric flux through one face of the cube. 36. An insulating sphere is 8.00 cm in diameter and carries a 5.70-?C charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with radius (a) r = 2.00 cm and (b) r = 6.00 cm. 44. A solid conducting sphere of radius 2.00 cm has a charge of 8.00 ?C. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of –4.00 ?C. Find the electric field at (a) r = 1.00 cm, (b) r = 3.00 cm, (c) r = 4.50 cm, and (d) r = 7.00 cm from the center of this charge configuration. 45. Two identical conducting spheres each having a radius of 0.500 cm are connected by a light 2.00-m-long conducting wire. A charge of 60.0 ?C is placed on one of the conductors. Assume that the surface distribution of charge on each sphere is uniform. Determine the tension in the wire.