Lecturer: Doug Folsom ( email: )
Office: Broida 6302
Office Hours: Monday 12:00-1:00, Wednesday 12:00-1:00, 2:00-3:00

TA: Andrew Merrill ( email: )
Office: Physics Study Room (Broida 1019)
Office Hours: Monday 2:30-4:30, Thursday 3:00-4:00

Textbook:

Halliday, Resnick, and Krane Physics, 5th edition, Volume 2

Course Outline:

Physics 24 is a continuation of Physics 23. This quarter we will continue to examine electricity and magnetism (E & M). We will cover magnetic induction, AC circuits, Maxwell's equations, and optics. The lectures will supplement the textbook; we will cover some sections in a different order and introduce extra examples.

Grading:

Grades will be based on 9 homeworks and 3 exams. The final exam will be non-cumulative and similar in length to the midterm exams.

Homework: 25%
Exams: 75% ( each is worth 25% )

Homeworks will be due in the Physics 24 box in the PSR at 5pm on Mondays and returned the following Monday. Late homeworks will receive reduced scores unless prior arrangements have been made with the TA.

Course Schedule:

Graded:
HRK Chapter 35 Exercise 6, Problem 2 (omit part c), Problem 6

Ungraded:
HRK Chapter 34 Problems 5, 6
HRK Chapter 35 Exercise 29, Problem 1

Graded:
HRK Chapter 34 Exercise 18 (omit part c), Problem 14
HRK Chapter 36 Problem 11

Ungraded:
HRK Chapter 34 Exercise 16, 26
HRK Chapter 36 Exercise 9, 10

Graded:
HRK Chapter 36 Exercise 47, Problem 10

1. In class, we listed 3 ways to write a real oscillating function x(t):

Show that these 3 are equivalent by:
a)solving for C and &phi in terms of B₁ and B₂
b)solving for A₁ and A₂ in terms of B₁ and B₂
(Hint: Keep in mind A₁ and A₂ are complex numbers! Use Euler's Law and trig identities. )

Ungraded:
HRK Chapter 36 Exercise 31, 49
HRK Chapter 36 Problem 13 (omit part c)

Graded:
HRK Chapter 37 Problems 3, 7
HRK Chapter 38 Exercise 9

Ungraded:
None

Graded:

1. In class, we showed how to change from the integral form of Gauss' Law to the differential form. Do the same thing for Maxwell's Equation number 3. i.e. show that:

Hint: Use a tiny square loop for the loop integral. To get the full vector equation, you will have to repeat this 3 times (when you have done it once, you can just quote your earlier results).


2. In class, we used the following on the way to deriving the existence of electromagnetic waves:
Show that this equation is true by writing out all the gradients, cross products, and dot products in vector form.


3. a) Plug an arbitrary function E = E₀ f( k_xx + k_yy + k_zz + &omega t ) into the wave equation. Show that the wave equation is satisified, no matter what f is ( do not use a specific f ), as long as k_x, k_y, k_z, and &omega are related appropriately.
Hint: Call the function f(u) and use the chain rule.

b) Show that the equation c = &lambda f is satisfied. How do &lambda and f relate to k_x, k_y, k_z, and &omega ?


Ungraded:
1. Show that the curl of the gradient of any scalar field is zero.

2. Show that the divergence of the curl of any vector field is zero.

Graded:
HRK Chapter 38 Exercise 16, Problem 11
HRK Chapter 39 Problem 12

Ungraded:
HRK Chapter 38 Problem 9
HRK Chapter 39 Exercise 25
HRK Chapter 39 Problem 3

Graded:
1. Prove that the ideal shape for a convex mirror is a parabola.
Hint: Place the tip of the mirror at the origin of a 2-D coordinate system. Pick a focal point a distance f away. Visualize light rays pointing away from the focal point and use these rays to find an equation relating y, x, and dy/dx of the mirror. Finally, plug in using a general parabola equation y = Cx² and show that you get a true statement.

2. Prove these equations using a convex lens as an example:
1) 1/o + 1/i = 1/f
2) m = -i / o
Assume all light rays have small angles of incidence.

HRK Chapter 40 Exercise 30

Graded:
HRK Chapter 40 Problem 7
HRK Chapter 41 Exercise 19
1. Consider a spherical mirror of radius R. Using a Taylor expansion to second order, show that the spherical mirror approximates a parabolic mirror and find the approximate focal length in terms of R.

Ungraded:
HRK Chapter 40 Problem 12
HRK Chapter 41 Exercises 2, 21

Graded:
HRK Chapter 41 Exercise 29, Problem 3
HRK Chapter 42 Problem 7 (omit part c)

Ungraded:
HRK Chapter 41 Problem 7
HRK Chapter 42 Exercise 29