AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
Magnetic Fields and Magnetic Forces
I.
Magnetic Fields
1. (I) Draw the magnetic Field Lines around the bar magnet shown below.
N
S
2. (I) Draw the magnetic field lines between the poles of the magnets shown below.
N
N
S
N
3. (I) Draw the magnetic field lines around a straight section of wire carrying a current horizontally
left.
I
4. (I) Draw the magnetic field lines around a straight wire carrying current that is moving directly
towards you.
I
II.
Magnetic Forces on Charged Particles
5. (I) Determine the magnitude and direction of the force acting on a proton traveling 3.58 × 106 m/s
horizontally west in a vertically upward magnetic field of strength 1.30 T.
6. (I) An electron with a speed of 1.80 × 106 m/s enters a 0.250 T magnetic field at an angle of 90°.
a. What is the magnitude of the force?
b. If the electron is moving north in a horizontal plane and the magnetic field is directed
vertically downward, what direction will the electron be deflected?
7. (I) Indicate the direction a proton will be deflected in the situations below. B is the magnetic field
and v represents the direction the proton is moving.
a)
B
8.
.
v
b)
XB
v
c) v
X
d)
B
B
e)
v
f)
B
v
.
v
B
(II) A proton moving at a speed of 9.5 m/s enters a magnetic field of strength 1.2 T at a right
angle. What is the acceleration of the proton in the magnetic field?
AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
9. (I) A 0.32 µC particle moves with a speed of 16 m/s through a region where the magnetic field
has a strength of 0.95 T. At what angle to the field is the particle moving when if the force
exerted on it is
a. 4.8 X 10-6 N
b. 3.0 X 10-6 N
10. (II) An electron moving perpendicular to a magnetic field of 4.6 X 10-3 T follows a circular path
of radius 2.80 mm. What is the speed of the electron?
11. (II) Derive an equation for the time T required for a particle of mass m and charge q to complete
one circular orbit in a magnetic field B. Your equation must be in terms of m, q, and B (constants
can be included).
12. (III) Two isotopes of Uranium, 235U (m = 3.90 X 10-25 kg) and 238U (m = 3.95 X 10-25 kg), are sent
into a mass spectrometer with a speed of 1.05 X 105 m/s as shown in the diagram below. Given
that each isotope is singly ionized, and the strength of the magnetic field is 0.750 T, what is the
distance between the two isotopes as they complete half a circular orbit?
13. (III) An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons. A
horizontal beam alpha particles is injected with a speed of 1.3 X 105 m/s into a region with a
vertical magnetic field of magnitude 0.155 T. How long does it take an alpha particle to complete
half a circle?
14. (I) A charged particle is projected with its initial velocity parallel to a uniform magnetic
field. The resulting path is a ____.
(A) spiral
(B) parabolic arc (C) circular arc
(D) straight line parallel to the field
(E) straight line perpendicular to the field
AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
For Questions 15-16
A proton traveling with speed v enters a uniform electric field of magnitude E, directed
parallel to the plane of the page, as shown in the figure above. There is also a magnetic
force on the proton that is in the direction opposite to that of the electric force.
15. Which of the following is a possible direction for the magnetic field?
(A)
(B)
(D)  (directed out of the page)
(C)
(E) (directed into the page)
16. If e represents the magnitude of the proton charge, what minimum magnitude of the
magnetic field could balance the electric force on the proton?
(A) E/v (B) eE/v (C) vE (D) eE (E) evE
17. In a region of space there is a uniform B field in the plane of the page but no E field. A
positively charged particle with velocity v directed into the page is subject to a force F in
the plane of the page as shown above. Which of the following vectors best represents the
direction of B?
(A)
(B)
(C)
(D)
(E)
18. A negatively charged particle in a uniform magnetic field B moves with constant speed v
in a circular path of radius r, as shown above. Which of of following graphs best
represents the radius r as a function of the magnitude of B, if the speed v is constant?
AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
III. Magnetic Forces on Current Carrying Wires
19. (I) Electric current is flowing through a copper wire.
a. What is the force per meter on the wire when carrying 9.8 A of current and is
inserted perpendicularly to a 0.80 T magnetic field?
b. What is the force if the angle between the wire and the magnetic field is 45°?
20. (I) A wire 1.5 m in length is carrying 6.5 A of current is oriented horizontally. At this
point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle of
40° to the wire. What is the magnitude of the force on the wire due to the Earth’s
magnetic field of 5.5 × 10-5 T at this point?
21. (I) How much current is flowing in a wire 4.2 m long if the maximum force on it is 0.9 N
when places in a uniform 0.0800 T field?
22. (II) The force on a wire carrying 25.0 A is a maximum of 4.14 N when placed between
the poles of a magnet. If the pole faces are 22 cm in diameter, what is the approximate
strength of the magnetic field?
23. (I)What is the magnitude of the magnetic field 1 m from a long straight wire carrying a
current of 1 A?
24. (II) A 52 µC particle moves parallel to a long wire with a speed of 720 m/s. The
separation between the particle and the wire is 13 cm and the magnitude of the force on
the particle is 1.4 x 10-7 N. What is the current flowing through the wire?
25. (II) A rectangular loop of wire of mass 10 grams hangs vertically as shown in the figure
below. A magnetic field is directed horizontally, perpendicular to the wire, and points out
of the page. The horizontal portion of the wire (length 0.1m) is near the center of the
magnetic field. The top portion of the wire loop is free from the field. The loop hangs
from a balance which measures a downward force of 0.128 N when the wire carries a
current of 0.2 A. What is the strength of the magnetic field?
26. (II) Compare and contrast a meter and a motor.
AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
27. (I) Two long wires are separated by a distance of 2d, as shown below. Both wires carry a
steady current into the page. At what points in the plane of the page (besides points at
infinity), is the magnitude of the magnetic field due to the currents zero?
a.
b.
c.
d.
e.
Only at point P
All points along the line connecting the wire
All points on the line SS’, a perpendicular bisector of a line connecting the two wires
All points on a circle of radius d centered at either wire
At no points expect infinity
28. (I)Two long, straight, parallel wires separated by a distance, d, carry equal currents, I,
toward the top of the page, as shown above. The magnetic field due to the wires at a point
halfway between them is _____.
(A) zero in magnitude
(B) directed into the page
(C) directed out of the page
(D) directed to the right
(E) directed to the left
29. (II)Two long, parallel wires, fixed in space, carry currents I1 and I2. The force of
attraction has magnitude F. What currents will give an attractive force of magnitude 4F?
(A) 2I1 and ½I2
(B) I1 and ¼I2
(C) ½I1 and ½I2
(D) 2I1 and 2I2
(E) 4I1 and 4I2
30. (II)Two very long parallel wires carry equal currents in the same direction into the page,
as shown above. At point P, which is 10 centimeters from each wire, the magnetic field is
_____.
(A) zero (B) directed into the page
(E) directed to the right
(C) directed out of the page
(D) directed to the left
AP® Physics 2
Myers Park High School
Problem Set: Magnetic Fields and Forces
Questions 31-32 relate to the two long parallel wires shown below. Initially the wires arc a
distance d apart and each has a current i directed into the page. The force per unit length on each
wire has magnitude Fo
31. (II)The direction of the force on the right-hand wire due to the current in the left-hand wire
is _____.
(A) to the right
(B) to the left
(C) upward in the plane of the page
(D) downward in the plane of the page
(E) into the page
32. (II)The wires are moved apart to a separation 2d and the current in each wire is increased
to 2i. The new force per unit length on each wire is _____.
(A) F0/4
(B) Fo/2
(C) Fo
(D) 2Fo
(E) 4Fo
1.
See Instructor
2.
See Instructor
3.
5.
7.45 x 10-13 N
North
6.
a) 7.2 x 10-14 N
b) East
7.
9.
a) 81o b) 38o
10.
2.26 X 106 m/s
See Instructor
a) right b) right
c) down d) out of
the page
e) zero f) up
2𝜋𝑚
11. 𝑇 =
4.
See Instructor
8.
1.1 X 109 m/s2
12. 1 cm
𝑞𝐵
13. 4.24 X 10-7 s
14. D
17. E
18. B
21. 2.68 A
22. 0.753 T
23. 2 x10-7 T
24. 2.4 A
25. 1.5 T
26. See Instructor
27. A
28. A
29. D
30. E
31. B
32. D
15. D
19. a) 7.84 N
b) 5.54 N
16. A
20. 3.45 x 10-4 N