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?
Goal: Reason about electric circuits
Source: 283-580 100-watt and 40-watt bulbs in series
Two light bulbs are connected to a wall outlet as shown below. Bulb #1
is 100W and Bulb #2 is 40W. Which statement is true?
(3) Since the resistance of the bulbs goes as the reciprocal of its
wattage, students can reason that the most power is dropped in the 40W
bulb. Another way to reason is this. Suppose the potential source was
such that the potential difference over the 40W bulb was 120V, i.e. its
normal operating condition. The potential difference over the 100W bulb
is then 48V, which means that it is operating at (48/120)2 of its normal
condition. The bulb is dissipating about 16W.
Goal: Hone understanding of series circuits.
Source: 283-575 Two bulbs in series
A light bulb is connected to a battery as shown in Figure A below. When
a second bulb is connected as shown in Figure B, what happens to the
brightness of the original bulb?
(2) Depending upon the bulbs and battery, the bulbs could appear to go
out.
Goal: Hone understanding of parallel circuits.
Source: 283-570 lights in parallel
A light bulb is connected to a battery as shown in Figure A below. When
a second bulb is connected as shown in Figure B, what happens to the
brightness of the original bulb?
(3) If the battery cannot sustain the potential difference the bulb will
dim somewhat. This can confuse students so any demonstration should not
use a marginal battery.
Goal: Reason regarding circuits
Source: 283-560 Circuit voltages
Consider the circuit below. How does the voltage difference between
points A and C compare to the voltage difference between points A and D?
VAC < VAD
VAC = VAD
VAC > VAD
Cannot be determined
(2) It is interesting to find out how many students recognized that the
comparison did not require the use of Ohm’s law. To gauge student
understanding it is interesting to ask questions such as; does any
current flow in the wire between C and D? If C and D are at the same
potential, why does any current flow?
Goal: Reasoning regarding circuits
Source: 283-565 circuit currents
Consider the circuit below. Which statement(s) is correct?
- IAB = IBD +
IBC- IBC < IBD
- IBC > IBD
(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.
Goal: Hone the relationship between E and V
Source: 283-475 Must V=0 if E=0?
True or false: it is possible to have the electric field be 0 at some
point in space and the electric potential be non-zero at that same
point.
(1) Whichever answer students give, ask them to draw a charge
configuration which satisfies their answer. Often this is sufficient to
cause them to change their mind. If appropriate raise for discussion the
case of the interior of a uniformly charged spherical shell.
Goal: Reason with electric fields
Source: 283-370 E due to circular rods
All of the curved charged rods shown in the image below have the same
radius and linear charge density (though some are positively charged and
others are negatively charged). For which configuration would the
magnitude of E at the origin be greatest?
(6) This problem constitutes a good exercise for students learning the
vector nature of the electric field. There are many good followup
questions, such as; Which configurations have zero field at the origin?,
Order the configurations by increasing magnitude of electric field at
the origin. Stress the value of symmetry for reasoning to the answer. A
negative distribution in a quadrant is equivalent to a positive
distribution in the opposite quadrant, which means that distributions #5
and #7 are equivalent (for purposes of finding the E field at the
origin).
Goal: Problem solving with rotational kinematics
Source: CT151.2S02-39
Two masses, attached to the ends of a rigid massless rod, are rotating
about pivot P as shown in the picture below. The mass two meters from P
has speed 0.5m/s. What is the acceleration of the mass one meter from
P?
(2) Every one of the possible wrong responses indicates a common error
that students make. After the problem has been discussed it is useful to
have students find the acceleration of the mass at 2m and see that the
accelerations are in the same ratio as the velocities. Drawing vector
diagrams showing the Δv for each mass is useful for explaining this
relationship.
Goal: Hone the concept of electric field
Source: 283-340 Where is E zero near a dipole? 9/21
Where,
other than at infinity, is the electric field 0 in the vicinity of the
dipole shown?
(5) Students have a lot of difficulty distinguishing electric field from
potential. Students already exposed to the concept of potential
frequently respond that the field is zero along the y-axis. If there are
many confused students, before identifying the correct response, it
helps to have the students draw the field lines.
Commentary:
Answer
(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.