# A2L Item 242

Goal: Reason regarding circuits

Source: 283 Compare dissipated power with inductors

Consider the following circuits. Two identical batteries are
connected to two identical inductors in series with different resistors.
The switch is closed at t=0. Which is true regarding the energy
supplied by the battery to establish current I?

1. The battery in A does more work.
2. The battery in B does more work.
3. Both batteries do the same work.
4. Cannot be determined

### Commentary:

(4) It is not determined that either circuit can achieve the current I.
If I is to be interpreted as the ‘final’ current, then the answer is #2.
The lower the resistance the higher the final current. There is more
energy stored in the inductor if the final current is higher. In
addition, the energy dissipated in the resistor goes as i2R which is
larger for circuit B for every current larger than V/(2R).

# A2L Item 237

Goal: Hone understanding of Faraday’s Law

Source: 283-715 bar with moving magnet

A
conducting bar is placed on a set of horizontal rails. A bar magnet is
positioned above the rails with its north pole facing the rails, and is
then released. While the magnet falls toward the rails, which of the
following statements are true.

1. There is an electric field in the
bar
2. There is a current in the bar
3. The bar remains
stationary
1. A only
2. B only
3. C only
4. A and B
5. A and C
6. B and C
7. A, B, and C

### Commentary:

(4) As the bar magnet falls, the magnetic flux through the circuit will
change. This will cause an E field and current in the conducting bar.
The conducting bar will also experience a magnetic force due to the
current flowing in the bar.

# A2L Item 234

Goal: Reason regarding forces between current elements

Source: 283-660 Force between two wires

A very long wire lies in a plane with a short wire segment. The long
wire carries current I, while the short wire of length L carries current
i. The two wires are parallel to each other. Which of the following
statements are true?

1. The direction of the magnetic force
exerted by the long wire on the short wire is directed away from the
long wire.
2. The magnitude of the force on the short wire is
μ0IiL/2πd.
3. The long wire experiences a force
of exactly the same magnitude as the force experienced by the short
wire.
1. A only
2. B only
3. C only
4. A and B
5. A and C
6. B and C
7. A, B, and C
8. None of them are true

### Commentary:

(6) The force is attractive between the wires so statement A is false.
Students need to interpret the phrase ‘very long’ as implying that the
wire is infinite.

# A2L Item 233

Goal: Reasoning regarding magnetic fields caused by current elements

Source: 283-655 Ordering magnetic field magnitudes

Order the following situations according to the magnitude of the
magnetic field at the point P. Order from highest to lowest.

1. ABCD
3. BDAC
5. DABC
6. None of the above

### Commentary:

(6) This question poses a good exercise for students. They can reason
comparatively without having specific expressions for the field
contributions from wires or loops. The order is CDBA.

# A2L Item 231

Goal: Reason regarding the fields due to current elements

Source: 283-650 Maximum B field

In all cases the wire shown carries a current I. For which situation
is the magnitude of the magnetic field maximum at the point P?

### Commentary:

(4) #4 is larger than #3 because contributions from the two half circles
reinforce in #4 rather than oppose each other as in #3. #4 is larger
than #1 because #4 has a half loop at half the radius. Situation #2
having a finite length of wire is a distracter. The field in #2 is
smaller than #3 and would be even if the wire in #2 were infinite. An
interesting follow-up is to ask students to well order the cases
according to the strength of the field.

# A2L Item 230

Goal: Applying the Biot-Savart law

Source: 283-645 Magnetic field from wire loop

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

1. 0
2. μ0I/4πR
3. μ0I/2πR
4. μ0I/4R
5. μ0I/2R
6. None of the above.

### Commentary:

(5) This question serves to identify students who do not know how to
apply the Biot-Savart law and/or those who are recalling the field due
to an infinite wire. This provides a good opportunity to discuss why
Ampere’s law is inappropriate for this case.

# 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 222

Goal: Reasoning regarding circuits

Source: 283-565 circuit currents

Consider the circuit below. Which statement(s) is correct?

1. IAB = IBD +
IBC
2. IBC < IBD
3. IBC > IBD
1. 1 only
2. 2 only
3. 3 only
4. 1 and 2
5. 1 and 3

### Commentary:

(4) Students should be encouraged to reason about the currents and not
calculate the value of the currents in circuits. Interestingly, if a
problem similar to this is given with the potential specified as a
number, many students will immediately calculate the currents.

# 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.