PHY2061
R. D. Field
Final Exam Solutions
Page 1 of
8
December 10, 2002
PHY 2061 Final Exam Solutions
Problem 1 (20 points):
Circle true or false for following (2 points each).
(a) (True or False)
The vector function
z
x
y
y
x
z
z
y
x
E
ˆ
ˆ
ˆ
)
,
,
(
−
+
=
r
represents a possible
electrostatic field with magnitude given by
2
2
2
)
,
,
(
z
y
x
z
y
x
E
+
+
=
.
Note that
0
ˆ
2
≠
=
×
∇
y
E
r
r
and hence this vector function cannot represent an electrostatic field since
all electrostatic fields have
0
=
×
∇
E
r
r
.
(b) (True or False)
The vector function
z
x
y
y
x
z
z
y
x
B
ˆ
ˆ
ˆ
)
,
,
(
−
+
=
r
represents a possible
magnetic field with magnitude given by
2
2
2
)
,
,
(
z
y
x
z
y
x
B
+
+
=
. Note that
0
1
≠
=
⋅
∇
B
r
r
and hence this vector function cannot represent a magnetic field since all
magnetic fields have
0
=
⋅
∇
B
r
r
.
(c) (True or False)
The electric field is zero on the surface of all conductors in static
equilibrium.
(d) (True or False)
It is possible to construct both electric and magnetic dipole field
configurations, but it is not possible to construct an electric monopole field.
(e) (True or False)
Lines of constant electric potential are always perpendicular to
electric field lines.
(f) (True or False)
In relativity, energy and momentum are conserved, but mass and
electric charge are not.
(g) (True or False)
When light moves from one medium to another both its speed and
wavelength change, but its frequency remains the same.
(h) (True or False)
It is possible for a proton to travel through water faster than light
travels through water.
(i) (True or False)
The real image created by a concave mirror is always inverted.
(j) (True or False)
Convex mirrors can produce both real and virtual images.
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PHY2061
R. D. Field
Final Exam Solutions
Page 2 of
8
December 10, 2002
Problem 2 (20 points):
Consider the situation illustrated in the
figure
.
A uniform
external
electric field points in the zdirection (
out of the paper
) with a value
given by
E
z
(t) =E
0
+ at
2
, where
E
0
= 808 V/m
and
a = 200 V/(m s
2
)
.
Also, a uniform
external
magnetic field points in the zdirection with a
value given by
B
z
(t) = B
0
+ bt
2
, where
B
0
= 8 T
and
b = 2 T/s
2
.
Both
external fields are confined to a circular region with a radius
R
, where
R
= 2 meters
. (c
2
= 1/(
µ
0
ε
0
),
c = 3 x
10
8
m/s,
µ
0
= 4
π
x
10
−7
Tm/A)
Part A (5 points):
What is the magnitude of the
induced
electric field (
in V/m
) at the point
P
on the
circumference of the circle of raduis
R
at the time
t = 2 seconds
?
Answer:
8
Solution:
We know from
Faraday's Law
that
∫
Φ
−
=
⋅
dt
d
l
d
E
B
r
r
.
If I choose my orientation to by counterclockwise then
Φ
B
= B
π
R
2
and
bt
R
dt
dB
R
R
RE
2
)
(
2
2
2
π
π
π
−
=
−
=
,
and solving for the
induced electric field E
gives
m
V
s
s
T
m
Rbt
R
E
/
8
)
2
)(
/
2
)(
2
(
)
(
2
=
−
−
=
−
=
.
Since
E
is positive the field lines point in the direction of my orientation (
counter
clockwise
).
Part B (3 points):
Which of the following gives the direction of the
induced
electric field lines at the point
P
on the circumference of the circle of raduis
R
at the time
t = 2 seconds
? (
circle one
)
(a) counterclockwise
(b) clockwise
Part C (4 points):
What is the magnitude of the
net
electric field (
in V/m
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 Physics, Magnetic Field, R. D. Field

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