# A2L Item 243

Goal: Hone the concept of line integral

Source: 283-CTQsas35

Three wires, each carrying the same current, I, are in a region of
space, as shown below. What could be the result of computing the left
hand side of Ampere’s law, , for the
three Amperian Loops shown?

1. Loop 1: μ0I, Loop 2: 2μ0I, Loop 3: 3μ0I
2. Loop 1: -μ0I, Loop 2: 0, Loop 3: μ0I
3. Loop 1: μ0I, Loop 2: 2μ0I, Loop 3: μ0I
4. Cannot be determined

### Commentary:

(4) The direction to integrate around the loop is not specified. The
only choice of responses that is possibly true is #2 and this would
require a clockwise integral around loop 1.

# A2L Item 229

Goal: Hone the right-hand-rule for vector cross products

Source: 283-640 B direction from wire loop

The diagram shows a circular wire loop of radius R carrying current I.
What is the direction of the magnetic field, B, at the center of the
loop?

1. Left
2. Right
3. Up
4. Down
5. None of the above

### Commentary:

(3) This is the best response given the choices. The question poses
little difficulty for students who have learned about the magnetic field
of current loops as a magnetic dipole. For these students this question
just confirms their knowledge. For students who are trying to apply the
Biot-Savart law to the loop as a set of current elements the question is
more challenging.

# A2L Item 228

Goal: Reason regarding electrodynamics

Source: 283-635 Path of a charge in E&B fields.

A
charge has an initial velocity parallel to the y-axis 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 a helical path.
4. The charge will travel in a 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:

(7) A common response is #4 because they forget that increasing pitch
implies that the speed changes.

# 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 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 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.