No Title

Instructions:

This is an open book, open note takehome exam, due Tuesday 5/7 by 5 pm. Feel free to ask me any clarifying questions on the problems, but do not consult otherwise with anyone on this exam. This exam is subject to the Emory Honor Code.

I will be available for office hours Thursday and Monday 3-4 pm, and we will meet in our usual timeslot (10:40 am in Dental 102) Tuesday morning for one last round of questions.

Summary:

Your NAME________________________

tex2html_wrap196

Your SCORE____

A hollow spherical shell carries charge density

in the region .
1. Find the electric field in the three regions (i) (ii) (iii) .
2. Find the electric potential in the three regions (i) (ii) (iii) .
A parallel plate capacitor has plates at and carries charge Q. A conducting plate of thickness is inserted midway between the capacitor plates.
1. Display quantitatively the charge distribution and electric field for this configuration. (That is, display, as a function of x, exactly where and how much charge is carried, and display both the magnitude and direction of . Neglect finite size effects in determining , and don't show a derivation.)
2. By what factor is the capacitance changed, when the conducting plate is inserted? (Show all your work.)
NOTE: The symmetry of this situation implies that .
1. What are the boundary conditions for V(x,y), at
  1. y=0
  2. y=a
  4. x=0
  5. Use your result for (iv) and the symmetry of the problem to state the boundary condition for x=0, solely in terms of values approaching zero from the right (positive values of x).
2. Solve Laplace's equation for in the region . Show all of your reasoning.
The potential at the surface of an infinitely long metal pipe, of radius R, is given by
1. Find the potential inside and outside the metal pipe.
2. What is the charge density on the pipe? (Assume there's no charge inside or outside the pipe.)
1. Taking the current density J to be constant for , find the induced magnetic field in three regions: (i) , (ii) , (iii) .
2. A rectangular current loop of height l, width a, and resistance R is placed to the right of the conducting pipe, with its left leg a distance from the center of the pipe. The current through the pipe increases at a constant rate, dI/dt = k.
  1. What current is induced in the loop, and in what direction does it flow?
  2. Explain why the direction of the induced current agrees with Lenz' law.
A solenoid carries the alternating current .
NOTE: Questions (a) and (b) are just a special case of homework 11, assigned problem 5 -- feel free to cite your result from there.
1. What is the magnetic field due to the solenoid current?
2. What, if any, electric field does this magnetic field induce?
3. What, if any, field is induced outside the solenoid by the changing field you calculated in (b)?