Download Worksheet on Conductors and Gauss Law

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.