Final Exam: Graduate Electromagnetics I, 95.657
Fall 2008, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question. In this section, you should be able to determine which answer
is correct using only physical argument and an understanding of the equations. No mathematical
calculations are necessary to answer any of the multiple choice questions.
1. What type of magnetic field
H
exists in a magnetostatics system that has no free currents?
(a) a curlless (irrotational) magnetic field
H
(b) a curling (rotational) magnetic field
H
(c) a zero magnetic field
H
(d) an oscillating magnetic field
H
2. The surface of a sphere is covered uniformly with a fixed electric charge and the sphere is spun
about its diameter at a constant frequency. What type of magnetic field does it generate?
(a) no magnetic field
(b) a
monopole magnetic field
(c) a dipole magnetic field
(d) a quadrupole magnetic field
3. What type of external magnetic field repels a small magnetic dipole?
(a) none, magnetic dipoles are never repelled
(b) a uniform magnetic field
(c) a very strong uniform magnetic field
(d) a nonuniform magnetic field with regions of high flux density
4. What gives rise to diverging electric fields?
(a) magnetic monopoles
(b) magnetic dipoles
(c) magnetic charges
(d) electric charges
5. What is the relationship between the potential energy
U
of a test charge in a static electric field and
the electric scalar potential
Φ
?
(a) the potential energy is proportional to electric scalar potential differences
(b) there are the exact same thing
(c) they are not related at all
(d) they are related by an inverse square law
6. A small round plate of electric charge sits in a region of free space with no boundaries. What
equation would be used to find the
exact
electric potential everywhere?
(a) Coulomb's law:
(b) the Laplace equation:
(c) the Green function solution:
(d) the first few terms of the multipole expansion:
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View Full Document7. A small round plate of electric charge is suspended in the middle of a hollow grounded metallic
sphere. What equation would be used to find the
exact
electric potential inside the sphere?
(a) Coulomb's law
(b) the Laplace equation
(c) the Green function solution
(d) the first few terms of the multipole expansion
8. Consider a point charge +
q
at the location (
x
=
a
,
y
=
a
), a point charge 
q
at
the location (
x = a, y
=
a
) and an semiinfinite grounded conducting plate
defined by the
x

z
plane. If we used the method of images to solve for the electric
potential, where should we place the image charge(s)?
(a) put a charge +
q
at (
x
=
0
,
y
= 
a
)
(b) put a charge +2
q
at (
x
=
0
,
y
= 
a
)
(c) no image charges required because the total charge is zero
(d) put a charge

q
at (
x
=
a
,
y
= 
a
) and a charge
+
q
at (
x
=
a
,
y
= 
a
)
9. Far away (
r
>>
a
)
from the system in the previous problem, how does the electric potential depend
on the distance
r
?
(a)
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 Spring '11
 Avery
 Magnetism, Mass, Magnetic Field

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