Physics 415: Electromagnetic Theory I
Prof. S. Teitel ----- Fall 2002

Midterm Exam

Please show all you work. Explain your steps to maximize your chances for partial credit. Put a circle around your final answer.

Problems 1, 2, and 3 are meant as "short answer" type problems. Once you see what is needed, you should not need to do a very lengthy calculation to arrive at the answer. Problem 4 is a more involved calculation. Note that Problem 4 is worth twice the points as the other problems.

  • Problem 1 [20 points total]

    a) Consider a point charge q in front of two infinite grounded planes at right angles to each other, as shown in the figure below. The intersection of the planes coincides with the z axis, and the position of the charge is given by the coordinates r=(xo, yo, 0). What is the force F on the charge q?


  • Problem 2 [20 points total]

    In each of the following examples, an electric field E is produced. In each case, this field will decay as E ~ 1/rn, for large r. Determine the value of n for each case, carefully explaining the reason for your answer.

    a) a spherical shell of radius R, centered on the origin, with a surface charge density of sigma(theta) = sigmaocos3(theta). Here sigmao is a constant, and theta is the usual spherical angular coordinate.

    b) a disk of radius R in the xy plane at z=0, centered on the origin, with surface charge density sigma(r) = Csin(2pir/R). Here r is the radial distance on the disk.

    c) four point charges located as follows:
    +q at r=(xo,yo,zo) -q at r=(-xo,yo,zo)
    +q at r=(-xo,-yo,zo) -q at r=(xo,-yo,zo)

  • Problem 3 [20 points total]

    a) A circular wire loop of radius R, carrying a current I, is bent at right angles, as shown below. What is the magnetic field B at a point r = r(ex+ey), where r>>R?   (ex and ey are the unit vectors in x and y directions)


    b) Two circular wire loops, each of radius R, are centered about the origin and lying in the xy plane. One loop is at height z=+a and has current I circulating clockwise. The other loop is at height z=-a and has a current I circulating counter-clockwise. For large distances r>>R the magnetic field B will decay, to leading order, proportional to B ~ 1/rn. What will be the value of n? You must explain your answer.

  • Problem 4 [40 points total]

    Consider a spherical shell of radius R, with a fixed surface charge density given by sigma(theta) = sigmaocos2(theta). Here sigmao is a constant, and theta is the usual spherical angular coordinate.

    Find the electrostatic potential phi(r) both inside and outside the shell.

Last update: Tuesday, August 21, 2007 at 1:49:04 PM.