Standards 0.1 & 0.2
Laura Andre
September 9, 2014
Problem
Use the complex expansion of cosine to derive the trigonometric identity for cos(a b).
Solution
The trigonometric identity we are trying to derive is:
cos(a b) = cos(a) cos(b) sin(a) sin(b)
(1)
The
Homework 2
Laura Andre
February 7, 2014
28.44
In Fig. 28-26, a metal wire of mass m = 24.1 mg can slide with negligible friction on two horizontal parallel
rails separated by distance d = 2.56 cm. The track lies in a vertical uniform magnetic eld of magni
Homework 4
Laura Andre
February 20, 2014
22.58
A certain electric dipole is placed in a uniform electric eld E of magnitude 40 N/C. Figure
22-58 gives the magnitude of the torque on the dipole versus the angle between the eld
E and the dipole moment p. Th
Homework 6
Laura Andre
March 13, 2014
5.3
For the long square conducting pipe in Example 1, suppose that the potential on the sides
at x = a/2 is 0, and that the potential on the sides at y = a/2 is V0 cos(x/a). Then
nd V (x, y) in the pipe, and sketch a
Homework 8
Laura Andre
April 16, 2014
9.12
A conducting slab, parallel to the xy plane and extending from z = a to z = a, carries
uniform free current density Jf = J0 THe magnetic susceptibility is 0 in the slab and m
i.
outside. Determine the magnetic el
Homework 9
Laura Andre
April 24, 2014
10.10
A metal disk of radius a, thickness d, and conductivity is located in the xy plane, centered
at the origin. There is a time-dependent uniform magnetic eld B(t) = B(t)k. Determine
the induced current density J(x,
Homework 7
Laura Andre
May 9, 2014
5.33
(a) Suppose on the surface of a sphere of radius R there is a surface charge density () =
0 cos2 , where 0 is a constant. What is V (r, ) inside and outside the sphere?
(b) Suppose now that () = 0 sin2 . What is V (
Homework 3
Laura Andre
February 14, 2014
29.48
In FIg. 29-71, a long circular pipe with outside radius R = 2.6 cm carries a (uniformly distributed) current
I = 8.00 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from the center.
Electricity and Magnetism
Final Exam
Laura Andre
May 10, 2014
1. (100 points)
A dielectric sphere of dielectric constant and radius a is located at the origin. There is
a uniform applied electric eld E0 in the x direction. The sphere rotates with an angul
Homework 1
Laura Andre
January 31, 2014
28.37
A proton circulates in a cyclotron, beginning approximately at rest at the center. Whenever it passes
through the gap between dees, the electric potential dierence between dees is 200V.
(a) By how much does it