the directions of the components of the
magnetic field from each conductor at the
point P?
What is the magnitude of each of the four
components BA, BB, BC, and BD at the point
P?
What is the magnitude of the magnetic field
at point P?
What is the direction of this resultant mag-
netic field?
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
This print-out should have 23 questions.
Multiple-choice questions may continue on
the next column or page – ﬁnd all choices
before answering.
001 (part 1 of 5) 10.0 points
A solid nonconducting cylinder of radius R
is very long. It contains a negative charge
evenly distributed throughout the cylinder,
with volume charge density ρ. Point P1 is
outside the cylinder at a distance r1 from its
center C and point P2 is inside the cylinder at
a distance r2 from its center C . Both points
are in the same plane, which is perpendicular
to the axis of the cylinder.
P1
3.
002 (part 2 of 5) 10.0 points
Using Gauss’s law, derive expressions for the
magnitude of the electric ﬁeld E in terms of
r , R, ρ, and fundamental constants for the
following case r > R (outside the cylinder).
1. E =
2. E =
r1
R
P2
On the cross-sectional diagram containing
P1 and P2 , select the vector diagram to indicate the directions of the electric ﬁeld at
points P1 and P2 .
P1
3. E =
4. E =
5. E =
6. E =
7. E =
8. E =
1.
C
C
P2
P1
C
r2
1
ρR
2
0r
ρ R2
2 0r
ρ R2
0r
ρR
2 0r
ρR
0r
ρ R2
2 0 r2
ρR
2 0 r2
ρ R2
2
0r
003 (part 3 of 5) 10.0 points
Using Gauss’s law, derive expressions for the
magnitude of the electric ﬁeld E in terms of
r , R, ρ, and fundamental constants for the
following case r < R (inside the cylinder).
P2
P1
1. E =
2.
C
2. E =
P2
3. E =
4. E =
5. E =
ρ
2 r2 0
ρ r2
20
ρ
2
r0
ρ
r0
ρr
20
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
6. E =
ρ r2
2
P1
0
7. E =
8. E =
ρ
2r
ρr
3.
0
P2
0
004 (part 4 of 5) 10.0 points
Another cylinder of the same dimensions, but
made of conducting material, carries a total
current I parallel to the length of the cylinder, as shown in the diagram above. The current density is uniform throughout the crosssectional area of the cylinder. Points P1 and
P2 are in the same positions with respect to
the cylinder as they were for the nonconducting cylinder.
005 (part 5 of 5) 10.0 points
Use Ampere’s law to derive an expression for
the magnetic ﬁeld B inside the cylinder in
terms of r , R, I , and fundamental constants.
1. B =
2. B =
P1
3. B =
r1
I
R
C
I
r2
P2
On the cross-sectional diagram containing
P1 and P2 in which the current is out of the
plane of the page (toward the reader), select
the vector diagram to indicate the directions
of the magnetic ﬁeld at points P1 and P2 .
P1
1.
C
P2
P1
2.
C
P2
C
4. B =
5. B =
6. B =
7. B =
8. B =
µ0 I
π
µ0 I
π
µ0 I
2π
µ0 I
2π
µ0 I
2π
µ0 I
π
µ0 I
π
µ0 I
2π
·
·
·
·
·
·
·
·
r2
R2
r
R
r2
R2
r
R2
r2
R
r
R2
r2
R
r
R
006 10.0 points
A coil of 228 turns carrying a current of
150 mA is wound on a ring with a rectangular cross section of inner radius 2.2 cm,
outer radius 8.9 cm, and height 2.2 cm.
If the ring has a magnetic permeability
µ = 2000 µ0 , what is the ﬂux through a cross
section of the ring?
Answer in units of µWb.
007 10.0 points
Two parallel copper rods are 0.9 cm apart.
Lightning sends a 10 kA pulse of current along
each conductor.
The permeability of free space is 1.25664 ×
10−6 N/A2 .
Calculate the force per unit length on one
conductor.
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
Answer in units of N/m.
008 10.0 points
Gauss’ law for magnetism tells us
1. the magnetic ﬁeld of a current element.
2. the net charge in any given volume.
3. that the line integral of a magnetic ﬁeld
around any closed loop vanishes.
4. that the magnetic monopoles do not exist.
5. that charges must be moving to produce
magnetic ﬁelds.
009 10.0 points
Consider two parallel wires where the magnitude of the left current is 2 I0 and that of
the right current is I0 . Point A is midway between the wires, and B is an equal distance
on the other side of the wires.
A
2.
3.
4.
5.
6.
BA
BB
BA
BB
BA
BB
BA
BB
BA
BB
BA
BB
=
2
3
=4
5
2
4
=
3
=
1
3
1
=
2
=
=9
P
2A×
B
0. 8 m
x
2A
C
Which of the diagrams correctly denotes
the directions of the components of the
magnetic ﬁeld from each conductor at the
point P ? The permeability of free space is
4 π × 10−7 N/A2 .
=3
=0
=2
010 (part 1 of 4) 10.0 points
Four long, parallel conductors carry equal 2 A
currents. A cross-sectional view of the conductors is shown in the ﬁgure. Each side of
the square has length of 0.8 m. The current
direction is out of the page at points indicated by the dots and into the page at points
indicated by the crosses.
y
A
D
×
2A
2A
B
The ratio of the magnitude of the magnetic
ﬁeld at point A to that at point B is
1.
BA
BB
B
8. A
BB
B
9. A
BB
B
10. A
BB
7.
3
BB
BC
1.
P
BA
BD
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
BD
013 (part 4 of 4) 10.0 points
What is the direction of this resultant magnetic ﬁeld?
BA
BB
2.
P
BC
1.
2.
BD
3.
3.
P
BC
BB
4.
BA
5.
6.
4.
P
BC
BB
BA
7.
BD
8.
BA
5.
9.
P
BC
BB
BD
BA
BB
6.
4
P
BC
BD
011 (part 2 of 4) 10.0 points
What is the magnitude of each of the four
components BA , BB , BC , and BD at the point
P?
Answer in units of T.
012 (part 3 of 4) 10.0 points
What is the magnitude of the magnetic ﬁeld
at point P ?
Answer in units of T.
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
Bnet
1
ı
= √ (−ˆ − ˆ)
2
is undetermined, since B = 0
= −ˆ
ı
1
ı
= √ (−ˆ + ˆ)
2
= +ˆ
1
= √ (+ˆ + ˆ)
ı
2
= −ˆ
= +ˆ
ı
1
ı
= √ (+ˆ − ˆ)
2
014 10.0 points
A solenoid 2.4 m long has a radius of 0.85 cm
and 900 turns. It carries a current of 4 A.
The permeability of free space is 4 π ×
10−7 T · m/A.
What is the approximate magnetic ﬁeld on
the axis of the solenoid?
Answer in units of mT.
015 (part 1 of 5) 10.0 points
A long, straight wire is in the plane of the
page and carries a current of 10 A. Point
P is also in the plane of the page and is a
perpendicular distance 0.2 m from the wire,
as shown below.
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
5
1. in the negative x-axis
P
x
0. 2 m
10 A
2. in the negative y -axis
z
3. in the positive y -axis
y
4. in the negative z -axis
y is upward
from the paper
With reference to the coordinate system in
the ﬁgure above, what is the direction of the
magnetic ﬁeld at point P due to the current
in the wire? The permeability of free space is
4 π × 10−7 T · m/A. Gravitational eﬀects are
negligible.
1. in the positive y direction
5. in the positive z -axis
6. in the positive x-axis
017 (part 3 of 5) 10.0 points
Determine the magnitude of the magnetic
force acting on the positive particle at point
P.
Answer in units of N.
018 (part 4 of 5) 10.0 points
An electric ﬁeld is applied that causes the net
force on the positive particle to be zero at
point P .
With reference to the coordinate system
established above, what is the direction of the
electric ﬁeld at point P that could accomplish
this?
2. in the negative x direction
3. in the positive z direction
4. in the negative z direction
5. in the positive x direction
6. in the negative y direction
1. in the positive z -axis
016 (part 2 of 5) 10.0 points
A 6.64 × 10−27 kg mass particle with positive
3.2 × 10−19 C charge is initially moving parallel to the wire with a 90 m/s speed when it
is at point P , as shown below.
6.64 × 10−27 kg
90 m/s
3.2 × 10−19 C
0. 2 m
10 A
2. in the negative z -axis
3. in the negative y -axis
4. in the positive y -axis
5. in the positive x-axis
x
z
y
y is upward
from the paper
With reference to the coordinate system
established above, what is the direction of the
magnetic force acting on the positive particle
at point P ?
6. in the negative x-axis
019 (part 5 of 5) 10.0 points
Determine the magnitude of the electric ﬁeld.
Answer in units of N/C.
020 (part 1 of 2) 10.0 points
The magnetic coils of a tokamak fusion reactor are in the shape of a toroid having an inner
radius of 1.036 m and outer radius of 1.877 m.
The toroid has 1310 turns turns of wire, each
of which carries a current of 8.42 kA.
beldorin (sb37529) – Homework 8 Sources of Magnetism – catala – (20491)
Find the magnetic ﬁeld strength along the
inner radius.
Answer in units of T.
021 (part 2 of 2) 10.0 points
What is the the magnetic ﬁeld strength along
the outer radius?
Answer in units of T.
022 (part 1 of 2) 10.0 points
A magnetic ﬁeld of 1.6 T is perpendicular to
a square coil of 16 turns. The length of each
side of the coil is 7 cm.
Find the magnetic ﬂux through an individual turn of the coil.
Answer in units of mWb.
023 (part 2 of 2) 10.0 points
Find the magnetic ﬂux through an individual
turn of the coil if the magnetic ﬁeld makes an
angle of 30 ◦ with the normal to the plane of
the coil.
Answer in units of mWb.
6
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