Physics 4C, Fall 2011, Homeworks

This page has homework assignments and solutions. They are all from the course textbook, Kip, Fundamentals of E&M,
Please don't look at the solutions until after you make a serious effort to solve the problems on your own.

First week: Chapter 1 problems:
Problems #: 1.1A, 1.1B, 1.1C, 1.2A, 1.2B, 1.3A, 1.3B, 1.4A, 1.5A, 1.6A
Solutions:
More problems: 2.1A, 2.1C, 2.1E, 2.1G, 2.7A
Solutions:

Second week: Chapter 2 problems:
Problems #: 2.1D, 2.1I
3) A non-conducting shell has inner radius a and outer radius b and total charge Q uniformly distributed over its volume. Find the electric field for a point at distance r from the center for r smaller than a, r between a and b, and r larger than b
4) Find the electric field for a long cylinder of radius R with charge density the same as the sphere of problem 2.1I, at radius r smaller than R and at r larger than R.
5) Same as problem 4) if the charge density is uniform instead.
6) Find the electric field for points inside and outside of a large flat slab of non-conducting material of thickness d and volume charge density rho.
7) A charge q is at the origin of coordinates. For a point on the x axis at distance d from the origin, show explicitely that the div(E)=0.
8) Calculate the div(E) for the electric field of a sphere of radius R and uniform charge density rho at a point at distance r=R/2 from the center and show that it satisfies Gauss' theorem.
Solutions:
More problems:
1) A conducting sphere of radius R has total charge Q. Find the surface charge density (&sigma) and the electric field right next to the surface, outside and inside, in terms of &sigma .
2) A conducting spherical shell has inner radius a and outer radius b, and total charge Q. There is also a point charge q at position r=a/2 along the x axis. Find the electric field at points (i) (x,y,z)=(2b,0,0),(ii) (x,y,z)=(-2b,0,0) and (iii) (x,y,z)=((a+b)/2,0,0).
Solutions:

Third week: Chapter 3 problems:
Problems #: 3.1A, 3.2D, 3.2E, 3.2F, 3.2G, 3.2H, 3.2I, 3.3A, 3.3B, 3.3D, 3.3E, 3.4A
Solutions:
More problems:
1) A conducting sphere of radius R and charge Q is connected by a conducting wire to another conducting sphere of radius 2R and charge 2Q that is at distance d>>R. Find the surface charge density for both spheres when equilibrium is reached.
2) A long insulating cylinder of radius R has volume charge density rho, uniformly distributed. Find the potential difference between a point at the lateral surface and a point at the center.
3) An electrostatic field has components E_x=4xy-2x, E_y=2x^2-4y. Find the difference in electric potential between points (x,y)=(0,0) and (x,y)=(a,b).
Solutions:

Fourth week: Chapter 4 problems:
Problems #: 4.1A, 4.1D, 4.1E, 4.2A, 4.2B, 4.3A, 4.6A, 4.6B, 4.6C, 4.6D, 4.6E, 4.7A
Solutions:
Additional problems (dielectrics): 5.3B, 5.3C, 5.4A, 5.4B
Solutions:

Fifth week: Chapter 6 problems:
Problems #: 6.1A, 6.1B, 6.1C, 6.3A, 6.3C, 6.4A, 6.4B, 6.4E, 6.5A, 6.5B, 6.6B
Solutions:
Solution to problem asked in class about equivalent resistance of cube edge, by Michael Nguyen

Sixth week: Chapters 11, 7, 8 problems:
1) Chpt. 11, problem 11.4C. Also study the material in pages 412, 413, 414 (RC circuits)
2) Show that in an RC circuit the energy dissipated in the resistor in the process of charging the capacitor equals the total energy in the capacitor after it is fully charged.
3) Consider Fig. 11.33 in the book (p. 412). Assume another resistor of the same magnitude R is connected in parallel to the capacitor. Compare the charge in the capacitor after a long time for the cases with and without the resistor connected in parallel.
4) Chpt. 7, problem 7.1A.
5) Chpt. 8, problems: 8.1A, 8.1C, 8.1D, 8.2A, 8.2C, 8.2D, 8.2K, 8.2M
Solutions:

Seventh week: Chapter 8 problems:
Problems #: 8.2B, 8.2E, 8.2F, 8.2G, 8.2I, 8.2J, 8.2O, 8.2P, 8.3B, 8.3C, 8.4A, 8.4B
Solutions:
correction to 8.2G solution:

Eighth week: Chapter 9 problems:
Problems #: 9.1A, 9.1C, 9.1D, 9.1E, 9.2A, 9.2C, 9.3A, 9.3B, 9.4B, 9.4C, 9.4D, 9.5A, 9.5B
Solutions:

Ninth week: Chapter 11 problems:
Problems #: 11.1A, 11.1B, 11.1C, 11.1E, 11.3A, 11.4A, 11.4C, 11.4D
Solutions:

Tenth week: Chapter 12 problems:
Problems #: 12.1A, 12.1B, 12.1C, 12.2A, 12.3A, 12.4A, 12.4B, 12.5A
Solutions: