Homeworks for PHY 352 K
CLASSICAL ELECTRODYNAMICS (I)

Welcome to the homework assignment page for Classical Electrosynamics (I) course (PHY 316) taught by Professor Vadim Kaplunovsky in Fall 2017 (unique #56365).

Most homework problems are taken from the Griffith's textbook Introduction to Electrodynamics; such problems are listed by their numbers in the textbook (page number in parentheses) according to the 4th edition. Note: if you have an older edition of the textbook, the problem numbers would be different!

If a homework set has any non-textbook problems, I shall either type it full at the appropriate place on this page, or else give a link to a separate TeX–generated PDF file.

By default, each problem is worth 10 points. But some problems may be worth more or fewer points; in that case I shall write down the pointage in brackets right after the problem number.

Once a homework is collected, I post the solutions in TeX–generated PDF format. The solutions will be linked to this page at the appropriate place.

Note: if for any reason you cannot come to the class on the day a homework is due, then scan your homework (or take a clear picture with a digital camera or cellphone) and email it to me and to the TA. Please don't waste time asking for my permission, just scan your work and email it, and make sure to do it before the end of the class on which the homework is due.

Homework Sets

Set 1

Reading assignments: textbook sections §1.1 and §1.4.

Textbook problems from chapter 2: 2.2 (page 62), 2.3 (page 65), 2.5 (page 65), 2.6 (page 65), 2.15 (page 76), 2.16 (page 76), 2.18 (page 76).

Textbook problems from chapter 1: 1.6 (page 8), 1.11 (page 15), 1.13 (page 15).

No non-textbook problems in this set.

Update 9/3: since some students have not got their textbooks yet, here is my transcription of the 10 homework problems.
Update 9/4: If you use my transcription, please download the file again; last time I missed a problem.

Due September 7 (Thursday); solutions.

Set 2

Textbook problems from chapter 1: 1.15 (page 18), 1.18 (page 20), 1.20 (page 20), 1.26 (page 24), 1.61 (page 56) [15 points], 1.62 (page 57) [15 points].

Textbook problems from chapter 2: 2.20 (page 80), 2.21 (page 83), 2.22 (page 83).

No non-textbook problems in this set.

Due September 14 (Thursday); solutions.

Set 3

Textbook problems from chapter 1: 1.46 (page 49–50), 1.48 (page 52), 1.49 (page 52).

Textbook problems from chapter 2: 2.48 (page 108), 2.53 (page 109) [20 points], 2.59 (page 112), 2.38 (page 102), 2.39 (page 102–103), 2.42 (page 104), 2.43 (page 107).

No non-textbook problems in this set.

Update 9/14 [9 PM]: Problem 2.50 was a typo for 2.59 (fixed). Problem 2.43 is postponed to the next homework set.

Due September 21 (Thursday); solutions.

Set 4

Textbook problems from chapter 2: 2.34 (page 95) [15 points], 2.35 (page 96), 2.37 (page 97) [15 points], 2.43 (page 107), 2.60 (page 112).
Notes for problem 2.60: (a) mind the induced charges; (b) in some printings, the textbook answer is a typo.

Textbook problems from chapter 3: 3.1 (page 118), 3.3 (page 119), 3.4 (page 119), 3.37 (page 160).
Notes: for problem 3.1, first read textbook §3.1.4 carefully; for problem 3.4, average the electric field as a vector.

No non-textbook problems in this set.

Due September 26 (Thursday); solutions.

Set 5

First, 4 textbook problems from chapter 3: 3.50 (page 164), 3.7 (page 129), 3.10 (page 130), 3.11 (page 130) [15 points].

Second, a reading assignment: textbook §3.2.4 (pages 127–129) about image charges from spherical surfaces. Note: I shall not explain this material in class.

Third, 2 more textbook problems from chapter 3 — 3.8 and 3.9 (both on page 129) — and a non-textbook problem:

• Work out the image charge method for a point charge located inside a grounded conducting spherical shell.
  (a) If the charge Q' is at distance b<R from the center, where is the image charge and what is its value?
  (b) Is there a net force on the point charge? If yes, find its magnitude and direction.
  (c) What happens if the conducting spherical shell is not grounded?
  [15 points]

Fourth, another reading assignment: textbook §3.3.1 (pages 131–140) about variable separation in Cartesian coordinates. While I shall explain this material in class in some detail, please read the textbook carefully to catch up the details I might miss.

Finally, 3 more textbook problems from chapter 3: 3.13, 3.14, and 3.15 (all on page 140).

Due October 5 (Thursday); solutions.

Set 6

First, 4 textbook problems from chapter 3: 3.17 (page 149), 3.19 (page 149), 3.26 (page 150) [12 points], 3.43 (page 162) [18 points].

Next, 2 non-textbook problems:

1. A thin spherical shell of radius R has a non-uniform charge density σ(θ,φ), but there are no charges outside on inside this shell. Inside the sphere, the potential is V(x,y,z)=kxyz for some constant k.
   (a) Rewrite this potential in spherical coordinates and exand it into a sum of terms of the form (const)×r^ℓ×Y_ℓ,m(θ.φ). For your convenience, here is the table of spherical harmonics.
   (b) Find the potential outside the spherical shell.
   (c) Find the surface charge density σ(θ,φ) os the spherical shell.
2. The Northern hemisphere of a solid ball of radius R has uniform charge density +ρ₀ while the Southern hemisphere has uniform density −ρ₀. Find the dipole moment of this ball and the potential it generates far away from the ball.

Finally, 4⃥ 3 more textbook problems from chapter 3: 3.29 (page 156), 3.30 (page 156), 3.46 (page 163), 3.53 (page 165).

Updated 10/12 at 7PM: Problem 3.46 is postponed to the next homework set.

Due October 17 (Tuesday); solutions [updated 10/21 at 21:20].

Set 7

First, 2 textbook problems from chapter 3 about electric multipoles: 3.46 (page 163) and 3.27 (page 154).

Next, 5 textbook problems from chapter 4 about dipole fields and forces (and torques) on dipoles: 4.4 (page 170), 4.5 (page 171), 4.29 (page 205), 4.6 (page 172) [15 points], and 4.30 (page 205).

Finally, 4⃥ 3⃥ 2 more textbook problems from chapter 4 about the bound charges and the displacement field: 4.10 (page 176), 4.13 (page 179) [15 points], 4.15 (pages 183–184), and 4.16 (page 184) [15 points].

No non-textbook problems in this set.

Update 10/17, 8:30 PM: Problem 4.16 is postponed to the next homework set.

Update 10/19, 5:20 PM: Problem 4.15 is also postponed to the next homework set.

Due October 24 (Tuesday); solutions.

Set 8

First, a reading assignment: textbook §4.4.2 and my notes, both on boundary problems in dielectrics. Make sure you follow all the examples in detail, including the examples not discussed in class.

Second, nine textbook problems from chapter 4: 4.15 (page 183), 4.16 (pages 183–4) [15 points], 4.41 (page 308), 4.19 (page 191), 4.36 (page 206–7), 4.37 (page 207) [15 points], 4.25 (page 197), 4.26 (page 202), 4.28 (page 204) [15 points].

No non-textbook problems in this set.

Due October 31 (Tuesday); solutions (updated 11/5).

Set 9

First, two reading assignments:

• Textbook example 5.2 (pages 212–214) about the cycloid motion in combined E and B fields.
• the wikipedia article about the cyclotron accelerators.

Second, two non-textbook problems:

1. (a) Write down the net kinetic+potential energy of a charged particle moving in combined E and B fields.
   (b) Verify that this net enegy is conserved in the cycloid motion from the textbook example 5.2.
2. A conducting cylinder of radius R and height H carries electric current of density J(x,y,z)=k(xx̂+yŷ-2zẑ), where k is a constant and the (x,y,z) coordinates are counted from the center of the cylinder's bottom disk.
   (a) Can this current be steady, i.e., time-independent?
   (b) What is the net current flowing through the cylinder? Through which surface does it flow into the cylinder and through which surface does it flow out?

Third, four textbook problems from chapter 5 about magnetic forces and electric currents:
       5.3 (page 216), 5.4 (page 223), 5.10 (page 228) [15 points], 5.6 (page 223).
Note: in problem 5.10, use textbook eq. (5.39) for the magnetic field and mind its non-uniformity!

Finally, four more textbook problems from chapter 5 about the Biot–Savart–Laplace Law:
       5.9 (page 228) [12 points], 5.11 (page 229), 5.12 (page 229) [12 points], 5.50 (page 259)[12 points].

Due November 9 (Thursday); solutions.

Set 10

Textbook problems from chapter 5:
       5.18 (page 240), 5.24 (page 248), 5.26 (page 248), 5.30 (page 249), 5.32 (page 251), 5.36 (page 255) [15 points], 5.58 (page 263).

Textbook problems from chapter 6:
       6.1 (pages 270–271), 6.4 (page 271) [15points].

No non-textbook problems in this set.

Due November 16 (Thursday); solutions.

Set 11

Reading assignments:

1. Notes on magnetic materials by Dr. Rudolf Winter (Aberystwyth University, Wales, UK):
   • Diamagnetism and paramagnetism
   • Paramagnetism in metals
   • Ferromagnetism
   • Magnetic–electric analogy
2. My notes «How to tell diamagnetic materials from paramagnetic».

Textbook problems from chapter 6:
6.8 (page 276), 6.10 (page 277), 6.12 (page 282), 6.13 (page 282), 6.20 (page 291).

Textbook problems from chapter 7:
7.1 (page 301), 7.2 (page 302), 7.3 (page 302), 7.5 (page 305).

No non-textbook problems in this set.

Due November 30 (Thursday); solutions (updated 12/7 at 8 PM).

Set 12

Textbook problems from chapter 7 about Faraday Law of Induction and related issues:
7.7 (page 311), 7.8 (page 311), 7.12 (page 316), 7.17 (page 320–321), 7.19 (page 321) [15 points], 7.51 (page 348) [15 points].

Textbook problems from chapter 7 about inductance and magnetic energy:
7.22 (page 327), 7.25 (page 327), 7.30 (page 331), 7.29 (page 331), 7.33 (page 322).

No non-textbook problems in this set.

Due December 7 (Thursday); solutions.

Exams

• First midterm exam, October 10; solutions.
• Second midterm exam, November 21; solutions.
• final exam, December 16.