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PHYS 222 Leader: Rosalie Leader: Dubberke Rosalie Class: PHYS 222 Course: PHYS 222 and Date: 9/7/2016 Worksheet 4 - Gauss’s Law Conductors Instructor: Dr. Paula Herrera-Siklódy Supplemental Instruction Iowa State University Date: 1/24/12 Useful Equations E q enclosed / 0 The uniform electric field flux relative to the charge Related Problems 1) A sphere of radius a = 2.0 cm with a uniformly distributed charge Q1 = 4.0 μC is at the center of a conducting spherical shell of radii b = 4.0 cm and c = 6.0 cm that has a total charge Q2 = −8.0 μC. (a) Find the electric field at point A, which is at r = 1.0 cm from the center of the system. (b) Find the electric field at point B, which is at r = 4.0 cm from the center of the system (c) Find the electric field at point D, which is at r = 8.0 cm from the center of the system 2) Negative charge, –Q, is distributed uniformly over the surface of a thin spherical shell with radius R. (a) Calculate the magnitude of the force the shell exerts on a positive charge q located a distance r > R from the center of the shell (outside the shell). (b) Calculate the magnitude of the force that the shell exerts on a positive point charge q located at a distance r < R from the center of the shell (inside the shell). Express your answers in terms of the variables q, Q, r, R, and constants π and Є 0. 3) A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated from its surroundings. (a) Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r < a. (b) Derive the expression for the electric field magnitude in terms of the distance r from the center for the region a < r < b. (c) Derive the expression for the electric field magnitude in terms of the distance r from the center for the r > b. (d) What is the surface charge density on the inner surface the shell? (e) What is the surface charge density on the outer surface the shell? (4) A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (see the Figure ). The inner shell has total charge +2q, and the outer shell has charge +4q. (a) Calculate the magnitude of the electric field in terms of q and distance r from the common center of the two shells for r < a. (b) Repeat part a with a < r < b. (c) Repeat part a with b < r < c. (d) Repeat part a with c < r < d. (e) Repeat part a with r > d. (f) What is the total charge on the inner surface of the small shell? (g) What is the total charge on the outer surface of the small shell? (h) What is the total charge on the inner surface of the large shell? (h) What is the total charge on the outer surface of the large shell? Express all answers in terms of q, r, a, b, c, d, π, and Є0.

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