Physics 200B Final Exam 22-Mar-04
Dr. Cebra Name: _________________
Instructions: Work all parts
of both problems (each problem worth 50 points). No notes, calculators, etc.
Please write your name on every page.
1. An inductor consists of two
concentric cylinders of length d and
radii a and b (assume that d >> b). Half the
volume between the cylinders is filled with a medium of permeability m1 and the other half with a
medium of permeability m2, as shown in the figure. Find the following for
each of two cases: 1) a current, I,
flow parallel to the axis of the cylinder and in opposite directions on the
inner and outer conductor, and 2) a current, I, flows counter clockwise in the inner cylinder and clockwise on
the outer.
a) Find the B and H fields.
b) Find the total magnetic
energy.
c) Find the total inductance.
Phys 200B Name: _________________
1. Consider a super-conducting
sphere in an otherwise uniform magnetic field, B0.
a) Determine the H field inside and outside the sphere.
b) Determine the bound surface
current KM.
c) Make a semi-quantitative
sketch showing the B field lines
inside and outside the sphere.
Phys 200B Name: _________________
3. A copper wire, with radius a, lies a distance d from, and parallel to, a large, grounded, conducting plate. The
wire carries a line charge density l.
a) Find E in all space.
b) Find the force of attraction between the wire and the plate.
c) What is the electric potential at the surface of the wire?
Phys 200B Name: _________________
4.
Consider an infinite grounded conducting sheet (lying in the x-y plane). A circular disk of radius R is cut out of this sheet, insulated
from the rest of the sheet, and held at a potential V0. (The half space Green's function would reflect both
an arbitrary point charge and its image charge.
a) Determine the electric
field, E, as a function of z along an axis through the center of
the hole and perpendicular to the charged sheet.
b) Determine the electric potential, F, for an arbitrary point along the z axis.
Phys 200B Name: _________________
5. The long range interaction between atoms and molecules is dominated by the electrostatic interactions between there multipole moments. In the case of neutral, spherically symmetric atoms or molecules, the interactions is called van der Waals attraction and has an r-6 dependence on the separation of the atomic centers. Classically, this is interpreted as the interaction between a fluctuating dipole moment in one atom that induces a dipole moment in the second atom, and vice versa. Although the average fluctuating dipole moment of a spherically symmetric atom vanishes, the mean square fluctuation does not.
a) Show that the instantaneous electric of dipole 1 (located at the origin) is
The dipole moment induced in atom 2 (located at r) is then p2 = a2E1(r), where a2 is the molecular polarizability.
b) The energy of the induced
dipole in the electric field of atom 1 is 
. Show that the instantaneous energy of the dipole-dipole
interaction is:
