PHY2061
12-10-04
Name:_______________________ ___
Closed book exam. A calculator is allowed, as is one 8.5
×
11” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit. Answers should be calculated to 2 significant digits. Exam is worth 100 points, 25% of your total grade.
UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.”
Sphere: S
=
4
π r
2 a b x x
+ a b y y
+ a b z z
V
=
4
3
π r
2
(
π =
3.1415927
a b y z
− b a y z
) x − ( e
= a b x z
− b a x z
K k
=
1
4
πε
= × 9 2
9 10 N m / C
= c
K
2
=
0
µ
4
π
0
= −
7
2
ε
0
= × −
12 2
8.8542 10 C / N m
2
c
=
.
× 8 m/s F =
K
µ
0
=
4
π k q q
1 2 r
2
) y r
12
=
−
19
C
+
( a b x y
− b a x y
E =
F q
0
−
6
ε v ∫
C
E
= −
N
∇ = x ˆ v ∫
S
Ε Α =
∂
∂ x d
Φ
B
B s =
= −∇
V dt
+
µ i
0 enc y ˆ
∂
∂ y
V
+
+ q enc
ε
0 z ˆ
∂
∂ z
µ ε
0 0
=
U q
0 d
Φ
E dt
= v ∫
C
µ
0
W
E s = −
∫
S v ∫
S
B ⋅ d Α = j A +
U
∫
C
F s div d dt
µ ε
0 0
=
∫
S
0 d dt
∂
F x
∂ x
⋅
∫
S
+
ρ
ε
0
∇ × E =
E ⋅ d
A ∇ × B =
∂
F y
∂ y
+
∂
F z
∂ z
−
∂ B
∂ t
µ ε
0 0
∂ E
∂ t
+
0
µ
0 j
V
∫
C
E s
) z
∫
V
∇ ⋅ F dV
= ∫ v
S
F ⋅ d Α ∫
S
( ∇ × F
) ⋅ d A = ∫ v
C
⋅
Q C V U
=
1
2
C
( )
2 =
Q
2
2 C
C eff
=
C
1
+
C
2
1
=
1
+
1
C C C eff 1 2
∆ = iR
R
= ρ
L
A
µ = i
A
∆
V
L
=
L di dt
τ =
RC
RC
2
P Vi i R
V
2
= = =
R i
= dq dt
τ = r × F
R eff
=
R
1
+
R
2
F = q ( E v B ) F = i L × B
τ = µ × B
U
µ B
F z
= µ z
1
=
1
+
1
R R R eff 1 2 d B = k i d s ×r r 3 dB z dz
L
=
N
Φ
B i
U
=
1
2
L i
2 u
2
=
U
=
B
V 2
µ
0
+
ε
0
E
2
2
τ =
LR
L
R
ω
LC
=
1
LC
∆
V
S
=
N
N
S
∆
P
V
P
Page 1 of 12

PHY2061
12-10-04
Name:_______________________ ___ c
=
.
× 8 m /s 1 eV
=
γ =
1
1
− v
2
/ c
2 t
= γ t u x
′ = u
1
± x
± vu c
2 v x p = γ m u u y
′ =
F = d p
/ d t
γ
0
L
−
19
=
L
γ
0
J t x
′ = γ
(
( )
′ = γ t
±
/ u y
1
± vu x c
2
E
2 4 = 2 − 2 2 m c E p c
= γ mc
2
2
)
K
= ( γ −
1
) m c
2 y
′ = y z
′ = z n
1 sin
θ
1
ω =
2
π f
= n
2 sin
θ
2 k
=
2
π
λ
S =
1
µ
0
×
λ f
= v
I
=
P
=
S av
A v n
= c n sin
θ =
λ d
Page 2 of 12

PHY2061
12-10-04
Name:_______________________ ___
1.
The electric field component of a traveling electromagnetic wave is described by
E =
E
0
( kx
− ω t
)
, where E
0
is a positive constant.
(a) [6 points] What is the magnetic field component, both magnitude and direction?
(b) [6 points] What is the average intensity of the wave per unit area perpendicular to the direction of the travel?
(c) [6 points] What is the wavelength of the traveling wave if the angular frequency
ω = 14
10 Hz ?
Page 3 of 12

PHY2061
12-10-04
Name:_______________________ ___
2.
[8 points] A light wave traveling horizontally strikes a glass prism with an index of refraction of n =1.5 as shown. The prism has a triangular cross section, with each interior angle measuring 60°. Calculate the angle relative to horizontal by which the light wave deflects after traversing both faces of the prism.
60°
Page 4 of 12

PHY2061
12-10-04
Name:_______________________ ___
3.
(a) [6 points] How much work is needed to accelerate a proton from a speed of
98.5% of the speed of light to 98.6% of the speed of light? The proton mass is
1.67 10
−
27
kg , and its charge is q e 1.6 10
−
19
C .
(b) [6 points] If the proton travels enters a region where there is a constant magnetic field of 0.5 T perpendicular to direction of motion at its final velocity of 0.986
c , what is the magnitude of the centripetal acceleration?
Page 5 of 12

PHY2061
12-10-04
Name:_______________________ ___
4.
[6 points] The electric field just outside of a spherical electric conductor of radius 3 cm is
E =
C r ˆ C
= × 4
, where 5 10 N/C . What is the net electric charge contained in the conductor?
Page 6 of 12

PHY2061
12-10-04
Name:_______________________ ___
5.
The electric field in a certain region of space is given by
E = xy
2 x + yx
2 ˆ .
(a) [6 points] What is electric charge density in this region?
(b) [6 points] What is the electric potential difference between 2 points on the x axis: x = 0 and x = a ?
Page 7 of 12

PHY2061
12-10-04
Name:_______________________ ___
6.
[6 points] Aluminum has a resistivity of
−
8
2.75 10 m . A length of wire is made by extruding 7 m of aluminum through a hole of diameter 4 mm. What will be the resistance of the wire?
7.
[8 points] A flat nonconducting surface infinite in extent carries a uniform charge density of
σ
7 10 C/m 2 . A small circular hole of radius R
=
1.5 m has been cut in the middle of the sheet as shown. Calculate the electric field at a point z = 5 m away from the center of the hole along an axis perpendicular to the surface. (In other words, consider z R , but don’t set exactly equal to zero. You may find the superposition principle handy.)
Z
R
(Space provided on next page)
Page 8 of 12

PHY2061
12-10-04
7. continued
Name:_______________________ ___
Page 9 of 12

PHY2061
12-10-04
Name:_______________________ ___
8.
[6 points] Two infinitely long straight wires have a circular cross section and are parallel to each other. One has a radius of 3mm and the other has a radius of 2mm.
They are covered with an insulating material of negligible thickness. The two wires are parallel to each other, but carry a current of 5A in opposite directions. If the central axes of each wire are separated by 5mm, calculate the magnitude of the magnetic field at a point 5mm to right of the center of the 2mm radius wire along the line joining the two axes, as shown:
3mm radius, current in
⊗
2mm radius, current out
:
Find field here
5mm 5mm
Page 10 of 12

PHY2061
12-10-04
Name:_______________________ ___
9.
A square loop of wire with a side length of 50 cm is rotated about an axis that bisects the square and that is perpendicular to a constant magnetic field of 0.5 T as shown
(the square loop extends into the plane of the paper). The rotational frequency is 60 revolutions per second.
B
⊗ i
ω axis :
(a) [6 points] Calculate the induced EMF in the loop of wire.
(b) [6 points] If the wire has a resistance of 0.5
Ω
, calculate the average power dissipated in the circuit.
Page 11 of 12

PHY2061
12-10-04
Name:_______________________ ___
10.
Consider the circuit below. Each capacitor has a capacitance of 2
µ
F, and each resistor has a resistance of 300
Ω
.
ε
+
(a) [6 points] Calculate the RC time constant of the circuit.
(b) [6 points] Once a 6 V battery is connected, how much time must elapse before the charge on the capacitors has reached half of the maximum value
(assuming they are initially uncharged)?
Page 12 of 12