Goal: Link energy conservation and electromagnetism
Source: 283-421 Change of total energy
A
uniform volume distribution of charge has radius R and total charge Q.
A point charge -q is released from rest at point b, which is a distance
3R from the center of the distribution. When the point charge reaches a,
which of the following is true regarding the total energy, E?
Goal: Hone the concept of electrostatic potential
Source: 283-420 Change of PE
A uniform volume distribution of
charge has radius R and total charge Q. A point charge -q is released
from rest at point b, which is a distance 3R from the center of the
distribution. When the point charge reaches a, which of the following is
true regarding the potential energy, U?
(7) Many students use an inverse square dependence appropriate
for fields. Others will take the field at b and multiply by the
displacement. Still others will assert that the potential doubles
because they are using the distance to the surface of the sphere.
Goal: Link flux to field lines.
Source: 283-415 nonzero flux?
The circles in the picture below are Gaussian surfaces. All other lines
are electric field lines. For which cases is the flux non-zero?
(2) As “follow-up” it is good to ask questions about comparisons
between two or more of the situations. For example, which is flux is
larger, a or f? Such questions help determine what students are focused
upon; are they keying on number of lines, do they understand that the
flux can be negative.
Goal: Link flux and enclosed charge.
Source: 283-410 Flux greatest?
Consider the flux through the following spherical Gaussian surfaces.
Take each charge distribution to be either a point charge or a spherical
shell of charge (uniformly distributed). For which situation is the flux
greatest?
(2) All these have the same flux. Some students do not read the question
carefully and think the number of ‘+’ signs matter.
Goal: Reasoning with electric fields.
Source: UMPERG-A2LEM7
The diagrams show two uniformly charged spheres. The charge on the
right sphere is three times as large as the charge on the left sphere.
Each vector represents the electric field at the center of one sphere
caused by the other sphere. Which choice best represents the
magnitude and direction of the electric field vectors caused by one
sphere at the position of the other sphere?
(5) The electric field at the sphere with smaller charge is three times
larger than the field at the sphere with larger charge.
Goal: Reasoning with Coulomb’s law
Source: UMPERG-A2LEM6
The diagrams show two uniformly charged spheres. The charge on the
right sphere is three times as large as the charge on the left sphere.
The arrows on each charge represent the force on the charge. Which
force diagram best represents the magnitude and direction of the
electric forces on the two spheres?
(4) By Newton’s third law the forces are equal and opposite.
Goal: Reasoning with electric forces
Source: UMPERG-A2LEM5
What is the direction of the electrical force on the charge q shown in
the diagram?
(3)
Goal: Problem solving with Coulomb’s law
Source: UMPERG-A2LEM4
What is the size of the electrical force on the charge q shown in the diagram?
(3) It is a common mistake to forget to take the y-component of the
force.
Goal: Reasoning with Coulomb’s Law
Source: UMPERG-A2LEM3
Three charges are positioned on the x-axis as shown. What is the
direction of the electrical force on the right-most charge?
(1) Students who forget to square the denominator in Coulomb’s law will answer (5).
Goal: Hone the vector nature of electric force.
Source: UMPERG-A2LEM2
Two charges, a negative charge Q, and a positive charge q, are
positioned as shown in the diagram. What is the direction of the
electrical force on q due to Q?
(3) The force is attractive.
Commentary:
Answer
(5) Students often forget to include the kinetic energy,
especially after a lot of discussion of potential energy. Many will
simply misinterpret the energy to mean potential energy. Teasing apart
these issues is important.