# A2L Item 227

Goal: Reason regarding electrodynamics

Source: 283-630 Path of a charge in E&B fields.

A
charge is released from rest in E and B fields. Both fields point along
the x axis. Which of the following statements regarding the charge’s
motion are correct?

1. The charge will travel along a straight-line path.
2. The charge’s speed will change as it travels.
3. The charge will travel in helical path.
4. The charge will travel in helical path of increasing pitch.
5. The charge will travel in a circle in the x-y plane.
6. 1 and 2 only
7. 2 and 4 only
8. None of the above

### Commentary:

(6) The different responses reveal the extent to which students
understand vector cross products and/or read the problem carefully. Some
students choose #8 because they do not like the way the motion is
expressed. They prefer descriptions such as, the charge first moves in a
straight line until it gets some speed then …

# A2L Item 226

Goal: Reasoning regarding the Lorentz force

Source: 283-620 Moving bar magnet and charge

A bar
magnet moving with speed V passes below a stationary charge q. What can
be said about the magnitude of the magnetic force on the bar magnet and
the charge q.

1. Fbar and Fq are both zero.

2. Fbar is zero and Fq is not zero.

3. Fbar is not zero and Fq is zero.

4. Fbar and Fq are both non-zero.

### Commentary:

(4) Many students have a lot of difficulty with this one. All of their
past experience has been with a moving charge in a magnetic field. They
may not think that it is equivalent to view the interaction from the
bar’s frame. Of course, they are correct, but the difference is
unimportant for purposes of recognizing that the force on the charge is
non-zero. They may invoke the third law by rote, without perceiving any
mechanism that could provide a force on the magnet. Discussing this in
some detail is a good idea.

# A2L Item 200

Goal: Distinguishing components of the Lorentz force

Source: 283 – effects of magnetic force

A charged particle moves into a region containing both an electric and
magnetic field. Which of the statements below are true?

1. The particle cannot accelerate in the
direction of B.
2. The path of the particle must be a circle.
3. Any change in the particle’s kinetic energy is caused by the E
field.
1. Only A
2. Only B
3. Only C
4. Both A&B
5. Both A&C
6. Both B&C
7. All are true.
8. None are true.

### Commentary:

(3) The only cases that most students see is the one having E and B
perpendicular. As a result they discount the case of E and B parallel
and think statement A is also true.

# A2L Item 198

Goal: Honing the right hand rule

Source: UMPERG-283 Mag Force

In a region of space there is a uniform magnetic field pointing in the
positive z direction. In what direction should a negative charge move
to experience a force in the positive x direction?

1. In the positive z direction
2. In the negative z direction
3. In the positive x direction
4. In the negative x direction
5. In the positive y direction
6. In the negative y direction
7. It can move in any direction
8. The force cannot be in the +x direction

### Commentary:

(6) Students will likely forget that the charge is negative.

# A2L Item 197

Goal: Reasoning with magnetic forces

Source: UMPERG-283-626

In the following situations a charge q moves in a uniform magnetic
field. The strength of the magnetic field is indicated by the density
of field lines. In all cases the speed of the charge is the same. For
which situation(s) will the charge q have the largest displacement in a
given time T.

1. 1
2. 2
3. 3
4. 4
5. 5
6. 1 & 3
7. 2 & 4
8. 1, 2, 3 & 4
9. 1, 2, 3, 4 & 5
10. Cannot be determined

### Commentary:

(5) Since the speed cannot change, the greatest displacement will occur
when the path is a straight line. Some students may answer #10 thinking
that the time matters.

# A2L Item 196

Goal: Reasoning with magnetic forces

Source: UMPERG-283-625

In the following situations a charge q moves in a uniform magnetic
field. The strength of the magnetic field is indicated by the density
of field lines. In all cases the speed of the charge is the same. For
which situation(s) will the charge q travel the greatest distance in a
given time T?

1. 1
2. 2
3. 3
4. 4
5. 5
6. 1 & 3
7. 2 & 4
8. 1, 2, 3 & 4
9. 1, 2, 3, 4 & 5
10. Cannot be determined

### Commentary:

(9) The magnetic force can change the direction of the velocity but not
the speed. The distance traveled, therefore, cannot depend upon either
the strength or orientation of the magnetic field. It is important to
have students who pick one of the other choices verbalize their reasons.
Some students may interpret the question as asking for the
‘displacement’ and, thinking that the time is needed, respond #10.
Actually the result for displacement is #5.

# A2L Item 184

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe148

A hoop
of mass 4 kg and radius 10 cm rolls without slipping down an incline
30° to the horizontal. The acceleration of the center of the hoop
is most nearly

1. 10 m/s2
2. 5 m/s2
3. 3.5 m/s2
4. 2.5 m/s2
5. none of the above
6. cannot be determined

### Commentary:

(4) Students should realize that the acceleration must be less
than a sliding mass on a frictionless surface would have which is #2.
Engage the students in a discussion of why the acceleration cannot

# A2L Item 181

Goal: Recognizing forces on current elements

Source: 283 Force on a half-loop

A
semicircular wire lies in a plane as shown. The positive z-direction is
out of the plane. The wire has current, I, in the counterclockwise
sense, and it is in a uniform external magnetic field, B, directed along
the +y axis. What is the direction of the net force, if any, acting on
the wire?

1. +x
2. -x
3. +y
4. -y
5. +z
6. -z
7. None of the above.

### Commentary:

(6) Since the current carrying semicircle lies in the x-y plane,
as does the magnetic field, the net force, if any, must point
perpendicular to the plane, or in the z direction. For the semicircular
wire, all force contributions add. There is no contribution to the net
force from current elements near the x-axis.

The force on the missing half of the loop would be out of the page.
Together both forces on a full loop would create a torque tending to
align the field of the current loop with the external field. If
appropriate relate this situation to the torque on a magnetic dipole.

# A2L Item 179

Goal: Recognizing the properties of magnetic fields

Source: 283 – field of wire

Oersted discovered that there is a magnetic field in the space
around wires carrying currents. Consider a long thin straight wire with
a current I. Which of the following statements about the magnetic field
lines is true?

1. Field lines are parallel to the
wire.
2. Field lines are perpendicular to the wire.
3. Field
lines are directed radially away from the wire.
4. Field lines are
circles centered on any point on the wire.
1. A only
2. B only
3. C only
4. D only
5. A and C only
6. B and D only
7. B and C only
8. None of them is true.

### Commentary:

(6) It is important to elicit reasons that students selected any
of the other responses. Rather than telling the correct answer have
students draw the field lines. Often they are able to reproduce pictures
they have seen but cannot describe the fields in words.

# A2L Item 180

Source: 283 field of bar magnets

Two
identical bar magnets are placed rigidly and parallel to each other as
shown. At what locations, if any, is the net magnetic field close to
zero?

1. A only
2. B only
3. C only
4. D only
5. A and B
6. A, B, and C
7. C and D
8. None of the above.