Instructor Survey:

Thank you for taking the time to answer and rate these assessment questions. The Colorado Upper-Division Electrostatics (CUE) Assessment is an instrument designed to test whether juniors successfully gain some of the key skills in E&M I. This survey asks you to both answer these questions (so that we may identify problems with the questions) and indicate whether you think that they adequately address the learning goals of the course.

First, you will be asked to answer the question. Where you are asked to sketch, describe the sketch you would draw as best as you can. Below each question we have listed a course learning goal, so you can get a better idea of where we feel each question fits into an electricity and magnetism course curriculum. After you answer each assessment question, please rate its quality by answering 3 follow up questions.

Name:
Institution:

Please Note: Once your information comes back to us, we will assign you a random number and will only reveal your answers and opinions in an anonymous manner.

SECTION 1: CHOOSING A METHOD

For each of the following 17 questions, give a brief outline of the EASIEST method that you would use to solve the problem. Methods used in this class include but are not limited to: Direct Integration, Ampere's Law, Superposition, Gauss' Law, Method of Images, Separation of Variables, and Multipole Expansion.

DO NOT SOLVE the problem, we just want to know:

• The general strategy
• Why you chose that method

 Example problem: Find the electric field at point P outside a uniformly charged sphere, with total charge +Q.

 Example Response: Gauss' Law with a spherical Gaussian surface centered around the origin. Because the E field is symmetric in theta and phi.

1. QUESTION 1
 An insulating sphere with radius R, with a voltage on its surface . Find E (or V) inside the sphere at point P.

2. Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
Students should recognize where separation of variables is applicable and what coordinate system is appropriate to separate in.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Coud be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

3. QUESTION 2
 A solid, neutral non-conducting cube, centered on the origin, with side length “a.” It has a charge density that depends on the distance z from the origin,, so that the top of the cube is strongly positive and the bottom is strongly negative, as in the figure. Find E (or V) outside, at point P (along the z axis).
4. Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
Students should be able to state Coulomb’s Law and use it to solve for E above a line of charge, a loop of charge, and a circular disk of charge.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

5. QUESTION 3

The same, neutral non-conducting cube as above, with, but where P is off-axis, at a distance r=50a.

6. Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
Students should be able to explain when and why approximate potentials are useful.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

7. QUESTION 4
 A grounded conducting plane with a point charge Q at a distance a. Find E (or V) at point P.
Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
Students should realize when the method of images is applicable and be able to solve simple cases.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

8. QUESTION 5
 A charged insulating solid sphere of radius R with a uniform volume charge p0, with an off-center spherical cavity carved out of it (see figure). Find E (or V) at point P, a distance 4R from the sphere.
Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form. (3) Techniques: Students should recognize that – in a linear system – the solutions may be formed by superposition of components.
Topic Learning Goal:
Students should recognize when Gauss’ Law is the appropriate way to solve a problem (by recognizing cases of symmetry; and by recognizing limiting cases, such as being very close to a charged body).

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

9. QUESTION 6
 A current loop of radius a that carries a constant current I. Find B (or A) at point P.
Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
(1) Students should be able to choose when to use Biot-Savart Law versus Ampere’s Law to calculate B fields, and to complete the calculation in simple cases. (2) Students should be able to recognize a current loop as a magnetic dipole, and that the B field of a dipole can be expressed as an approximation.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

10. QUESTION 7
 A solid non-conducting sphere, centered on the origin, with a non-uniform charge density that depends on the distance from the origin, where a is a constant. Find E (or V) inside at point P.
Response:

Course Learning Goal: (1) Problem-solving: Students should be able to choose the problem-solving technique that is appropriate to a particular problem. They should be able to apply these problem-solving approaches to novel contexts (i.e., to solve problems which do not map directly to those in the book), indicating that they understand the essential features of the technique rather than just the mechanics of its application. They should be able to justify their approach for solving a particular problem. (2) Communicaton: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.
Topic Learning Goal:
Students should recognize when Gauss’ Law is the appropriate way to solve a problem (by recognizing cases of symmetry; and by recognizing limiting cases, such as being very close to a charged body).

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

SECTION 2: GENERAL QUESTIONS

11. QUESTION 8
 A mass density is given by , where m is a constant. .
 What is the value of ?
Response:

 What physical situation does this mass density represent?
Response:

Course Learning Goal: Math/physics connection: Students should be able to explain the physical meaning of the formal and/or mathematical formulation of and/or solution to a junior-level electromagnetism problem. Students should be able to achieve physical insight through the mathematics of a problem.
Topic Learning Goal:
Students should be able to evaluate the integral from negative infinity to infinity of the delta function, d(x).

1. How well do these questions test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in these questions scientifically accurate?
a) Yes
b) Not completely
c) No

3. Are these questions written clearly and precisely?
a) Yes
b) Could be improved
c) No

12. QUESTION 9
 You are given a non-conducting sphere, centered at the origin. The sphere has a non-uniform, positive and finite volume charge density ρ(r). You notice that another student has set the reference point for V such that V=0 at the center of the sphere: V(r=0)=0. What would V=0 at r=0 imply about the sign of the potential at r→∞? (a) V (r→∞) is positive (+) (b) V (r→∞) is negative (-) (c) V (r→∞) is zero (d) It depends
Response:

Course Learning Goal: Math/physics connection: Students should be able to translate a physical description of a junior-level electromagnetism problem to a mathematical equation necessary to solve it. (2) Communication: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form (3) Expecting and checking solutions: When appropriate for a given problem, students should be able to articulate their expectations for the solution to a problem, such as direction of the field, dependence on coordinate variables, and behavior at large distances.
Topic Learning Goal: Students should be able to defend the choice of a suitable reference point for evaluating V (generally infinity or zero).

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

13. QUESTION 10
 You are given an infinite solid conducting cylinder whose vertical axis runs along the y direction, that is placed in an external electric field, , as in the figure to the right. The cylinder extends infinitely in the +y and –y directions. On the two-dimensional figure below: (a) Sketch the induced charge, σ. (b) Sketch the electric field everywhere.
Response:

Course Learning Goal: Visualize the problem: Students should be able to sketch the physical parameters of a problem (e.g., E or B field, distribution of charges, polarization), as appropriate for a particular problem.
Topic Learning Goal:
Students should be able to sketch the induced charge distribution on a conductor placed in an electric field. Students should be able to explain what happens to a conductor when it is placed in an electric field, and sketch the E field inside and outside a conducting sphere placed in an electric field.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

14. QUESTION 11
 For the conducting cylinder shown above we want to use the method of separation of variables to solve for: (a) the potential everywhere and (b) the surface charge sigma. List the boundary conditions on V and/or E at the surface needed to do this. Do not solve for V, just tell us the boundary conditions on V or E.
Response:

Course Learning Goal: Math/physics connection: Students should be able to translate a physical description of a junior-level electromagnetism problem to a mathematical equation necessary to solve it.
Topic Learning Goal: Students should be able to apply the physics and symmetry of a problem to state appropriate boundary conditions.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

15. QUESTION 12
 The following set of problems refers to the uniform flat, thin disk of radius R carrying uniform positive surface charge density +σ0 as in the figure.
 What is the value of the z-component of the electric field (Ez) very near the origin (z<
Response:

Course Learning Goal: Approximations: Students should be able to recognize when approximations are useful, and use them effectively (eg., when the observer is very far away from or very close to the source).

1. How well does this question test student achievement of the learning goal?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

 How does Ez behave as a function of z as you get very far from the disk (z>>R)?
Response:

Course Learning Goal: Approximations: Students should be able to recognize when approximations are useful, and use them effectively (eg., when the observer is very far away from or very close to the source).

1. How well does this question test student achievement of the learning goal?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

 Draw a qualitative graph of Ez as you move away from the disk, along the z-axis. We are looking for the relative magnitude and sign of Ez as a function of distance from the disk, not field lines. Include both z>0 and z<0 on your graph.
Response:
 Draw a qualitative graph of V as you move away from the disk, along the z-axis. Include both z>0 and z<0.
Response:
 What is a physical interpretation of the behavior of E (or V) near the origin?
Response:

Course Learning Goal: (1) Visualize the problem:. Students should be able to sketch the physical parameters of a problem (e.g., E or B field, distribution of charges, polarization), as appropriate for a particular problem. (2) Expecting and checking solution: When appropriate for a given problem, students should be able to articulate their expectations for the solution to a problem, such as direction of the field, dependence on coordinate variables, and behavior at large distances. For all problems, students should be able to justify the reasonableness of a solution they have reached, by methods such as checking the symmetry of the solution, looking at limiting or special cases, relating to cases with known solutions, checking units, dimensional analysis, and/or checking the scale/order of magnitude of the answer.

1. How well do these questions test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in these questions scientifically accurate?
a) Yes
b) Not completely
c) No

3. Are these questions written clearly and precisely?
a) Yes
b) Could be improved
c) No

16. QUESTION 13
 You are given a 2-D box with potentials specified on the boundary as indicated in the figures below. The general solution to Laplace’s equation in Cartesian coordinates is OR . That is, you can choose to associate the sin and cos with either the x or y coordinate. To solve this by separation of variables, which form of the solution should you choose? a) b) c) It doesn't matter.

Response:

Course Learning Goal: Math/physics connection: Students should be able to translate a physical description of a junior-level electromagnetism problem to a mathematical equation necessary to solve it.
Topic Learning Goal: Students should be able to apply the physics and symmetry of a problem to state appropriate boundary conditions.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

17. QUESTION 14
 A dielectric is inserted into an isolated infinite parallel plate capacitor, as shown.
 Using concepts and terminology you’ve learned in Phys3310, explain how the insertion of the dielectric reduces the electric field in the capacitor.
Response:

Course Learning Goal: Communication: Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form.(2) Deepen understanding: Students should deepen their understanding of Phys 1120 material. I.e., the course should build on earlier material.
Topic Learning Goal: Students should be able to explain what happens to a dielectric, when it is placed in an electric field. Students should be able to sketch the direction of D, P, and E for simple problems involving dielectrics.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

 What physical quantities would change (and how) in the limit that the dielectric constant approaches that of a perfect conductor?
Response:

Topic Learning Goal: Students should be able to describe similarities and differences between a conductor and a dielectric.

1. How well does this question test student achievement of the learning goal?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

18. QUESTION 15
 Circle all of the following boundary conditions that are suitable for solving Laplace’s equation for finding V(r,θ) everywhere due to a charge density σ on a spherical surface of radius R. (I) Vin=Vout at r=R (II) at r=R (III) at r=R (IV) at r=R
Response:

Course Learning Goal: Problem-solving techniques: Students should be able to choose and apply the problem-solving technique that is appropriate to a particular problem.
Topic Learning Goal: Students should be able to state the appropriate boundary conditions on V in electrostatics and be able to derive them from Maxwell’s equations.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

19. QUESTION 16
 You are given the following charge distribution made of 4 point charges, each located a distance “a” from the x- and y-axis. Is the dipole moment of this distribution zero? (a) Yes (b) No (c) Not sure
Response:

Course Learning Goal: Techniques: Students should recognize that – in a linear system – the solutions may be formed by superposition of components.
Topic Learning Goal: Students should be able to go between two representations of dipoles – as point charges, and as generalized dipole vectors – for simple charge configurations. Students should be able to calculate the dipole moment of a simple charge distribution.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

20. QUESTION 17
 Consider an infinite non-magnetizeable cylinder with a uniform volume current density J. Where is the B field maximum? Explain how to determine this.
Response:

Course Learning Goal: (1) Problem-solving techniques: Students should be able to choose and apply the problem-solving technique that is appropriate to a particular problem. (2) Math-Physics connection: Students should be able to translate a physical description of a junior-level electromagnetism problem to a mathematical equation necessary to solve it. Students should be able to explain the physical meaning of the formal and/or mathematical formulation of and/or solution to a junior-level electromagnetism problem. Students should be able to achieve physical insight through the mathematics of a problem.
Topic Learning Goal: 3. Students should be able to choose when to use Biot-Savart Law versus Ampere’s Law to calculate B fields, and to complete the calculation in simple cases. Students should be able to draw appropriate Amperian loops for the cases in which symmetry allows for solution of the B field using Ampere’s Law (ie., infinite wire, infinite plane, infinite solenoid, toroids), and calculate Ienc.

1. How well does this question test student achievement of the learning goals?
a) Well
b) Could be improved
c) Not well

2. Is the information given in this question scientifically accurate?
a) Yes
b) Not completely
c) No

3. Is this question written clearly and precisely?
a) Yes
b) Could be improved
c) No

Thank you for taking the time to answer these assessment questions.

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