Instructor Survey:

Colorado Upper-Division Electrostatics (CUE) Assessment

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:

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
    Without any calculations, write the general solution to the following differential equations. Express your answer with arbitrary constants, if necessary.
    For this question, A and B are real constants.

    2. (a)[insert equation]

    (b)[insert equation]

    (c) Describe or draw a specific physical situation where the differential equation [insert equation]might be applicable. Please give an explanation to justify your answer.


    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?
      not answered
      a) Well
      b) Coud be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  2. QUESTION 2
    An astronaut is in orbit around the Earth at a distance of R from the center of the Earth. Another astronaut is in a closer orbit at a distance R - d The difference in the strength of the gravitational field between the astronauts is given by,
    [insert equation]
    You are interested in predicting the difference in the strength of the gravitational field, when the astronauts are close to each other. Describe how you would simplify △g. For what choice of variable would be justifed in neglecting higher order terms? Explain your choice briefly but clearly.
    3. 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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  3. QUESTION 3

    Below is a plot of the potential energy, in Joules, of a particle free to move on a 2-d plane.

    4. (a) For which of these points (A-F) is the particle in stable equilibrium?

    (b) Please explain how you decided on the above answer:

    (c) Rank the magnitude of the gradient at the above points, from largest to smallest. (If some points have gradients with equal magnitude, please make that clear in your answer.)

    (d) Draw vectors that represent the force, [insert equation], at points A-F on the diagram above. Please make sure that the relative magnitude of your vectors is consistent among the points. Please indicate clearly if [insert equation] = 0 at any of the points.

    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  4. QUESTION 4
    Given this differential equation: [insert equation]
    The solution (for a particular set of positive coeffcients a1, a2, and a3) is shown below:
    (a) If x(t) represents the motion of a mass on a spring, and each term (for example, a1ẍ) has units of force, what are the units of "a1"

    (b) What aspect of the physical situation does "a3" describe?

    (c) Sketch the solution, on the axes below, if a3 is slightly smaller (but still positive) in [insert equation] and everything else is the same. (Note the original solution above is drawn below for reference.)

    Explain in words briefly what is different between your sketch and the reference case.

    (d) If we replaced the "0" in the differential equation [insert equation] with some function g(t), what would g(t) represent physically?


    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  5. QUESTION 5
    Please fill in the blanks so that the following correctly describe simple harmonic motion:
    (a) A restoring force that is proportional to

    (b) x(t) (position as a function of time) =

    (c) Draw U(x) - potential energy as a function of position. Describe any signifcant features of your graph.



    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  6. QUESTION 6
    A ball slides without friction in the bottom of a sawed off sphere of radius a (as pictured to the right). The ball is moving downhill with a known speed
    of magnitude v0and is at a known angle from the horizontal of θ.
    (a) Draw the vectors [insert equation] and [insert equation] on the picture to the a right.
    (b) Express the velocity vector [insert equation] in the i>x - y and r - θ coordinate systems in terms of a, θ, and v0. (i.e., [insert equation] and [insert equation], what are vx, vy, vr,vθ?) Please show your work.

    (c) For the x-y coordinate system, check that your answer makes sense by considering some particular value of θ.



    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  7. QUESTION 7
    I have a mass on a frictionless spring. If I pull the mass out and let it go, it oscillates with a natural frequency ωf . I attach this mass to a driving force F(t) = B sin(ωdt), where ωd can be adjusted. I also add a small amount of friction to the system. Draw a rough graph of the amplitude of the oscillation of the mass as a function of the driving frequency, ωd (assume you measure the amplitude after all transients have died out). Identify any major features. Don't worry about being exact.

    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  8. QUESTION 8
    Which Fourier series is the correct expansion for the function f(x)?

    (a) Choose your answer below.
    A) [insert equation]
    B) [insert equation]
    C) [insert equation]
    D) [insert equation]
    E) [insert equation]

    (b) Please explain your answer above briefly but clearly.


    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  9. QUESTION 9
    You plan to solve Laplace's equation in Cartesian coordinates, [insert equation], with given boundary conditions using the technique of separation of variables. How would you separate U

    A) [insert equation]
    B) [insert equation]
    C) [insert equation]
    D) [insert equation]
    E) [insert equation]
    F) None - Separation of variables only applies to ordinary differential equations.
    G) Other - write it here:

    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  10. QUESTION 10
    A particle (mass, m) is confined to move on the x-axis. There are two objects on the x-axis that attract this particle. One object is located at x = 0 and the attractive force between the object and the particle is proportional to the square of the distance between them (proportionality constant c). The second object is located at x = 10, and the attractive force between the object and the particle is inversely proportional to the distance between them (proportionality constant k). Consider an particle that is confined to the region between the two repulsive objects. Write down a differential equation that describes the position of the particle as a function of time, x(t).


    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


  11. QUESTION 10
    Consider an infinitely thin cylindrical shell with non-uniform mass per unit area of (; z). The shell has height h and radius a, and is not enclosed at the top or bottom.

    (a) What is the area, dA, of the small dark gray patch of the shell which has height dz and subtends an angle d[] as shown to the right?


    (b) Write down (BUT DO NOT EVALUATE) an integral that would give you the MASS of the entire shell. Include the limits of integration.


    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?
      not answered
      a) Well
      b) Could be improved
      c) Not well

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

    3. Is this question written clearly and precisely?
      not answered
      a) Yes
      b) Could be improved
      c) No

    4. Please make any additional comments or suggestions about this question here:


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

    If you have any additional comments about this survey as a whole, please enter them here:



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