Download PHYS 520B - Electromagnetic Theory

SPRING 2016
PHYS
February 16, 2016
520B - Electromagnetic Theory
Problem Sheet 2
Deadline March 1
When answering a problem, define any symbols that you introduce, discuss any
assumptions or approximations that you use, and provide appropriate discussions,
explanations, and references.
Q. 1
Jackson problem 6.23.
Notes: This is a gauge transformation problem. You will need to refer to section 6.13 to
guide you.
Q. 2
Jackson 6.5, parts (a) and (b).
Notes: Pay particular attention to the last short question to (a). For (b), you may want
to refer to section 5.6 for guidance.
Q. 3
Consider a coaxial cable, of radii a and b (a < b), carrying a current I. Using explicit
expressions for the electric and magnetic fields, evaluate the Poynting vector. Don’t forget
direction. Show that the power, P , is, as expected, P = IV , where V is the electrostatic
potential.
Q. 4
Consider an infinite half plane of a dielectric medium of permittivity ǫ, or equivalently
electric susceptibility χe . A point charge q is located in the empty space at a distance d
above the coordinate origin. This question asks you to find the force acting on the point
charge using the method of the Maxwell stress tensor. Once you obtain your final result you
may want to check your result through more traditional/textbook means.
(i) Use the method of images to derive an expression for the polarization surface charge
density. [Hint: This first part is a refresher on the textbook material covered in section
4.4.]
(ii) Now that you have the surface charge density, find the electric field and construct the
Maxwell stress tensor. Remember to consider the symmetry of the problem and retain
only those components that will survive.
(iii) Finally, put all the pieces together and evaluate the force acting on the point charge
by choosing an approrpriate surface of integration.