Chapter HW 3 D U E DATE 15 May 22th 1. A charge is located at the center of a regular tetrahedron (a four-sided surface) as in the figure below. Find (a) the total electric flux through the tetrahedron (b) the electric flux through one face of the tetrahedron 2. This figure shows the electric field lines for two point charges separated by a small distance. (a) Determine the ratio (b) What are the signs of and ? 3. A point charge is located at the center of a spherical shell of radius that has a charge uniformly distributed on its surface. Find the electric field (a) for a point outside the spherical shell with distance from the center. (b) for a point inside the shell a distance from the center. 4. Two small beads having positive charges and are fixed at the opposite ends of a horizontal insulating rod of length . The bead with charge is at the origin. As shown in the right figure, a third small charge bead is free to slide on the rod. At what position is the third bead in equilibrium? 5. A solid, insulating sphere of radius has a uniform charge density throughout its volume and a total charge . Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are and as shown in the right figure. We wish to understand completely the charges and electric fields at all locations. - 1 - (a) Find the charge contained within a sphere of radius (b) Form this value, find the magnitude of the electric field for (c) What charge is contained within a sphere of radius when ? (d) From this value, find the magnitude of the electric field for when . (e) Now consider when . What is the magnitude of the electric field for this range of values of ? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surface of radii , and . Which of these surfaces has the largest magnitude of surface charge density? - 2 -
