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CLF Preliminary Activities

Module by: George Brown

Summary: Preliminary activities for the PLTL workshop on Coulomb Law Forces. Intended as part of introductory undergraduate physics course on electricity and magnetism.

Activities Prior to Peer Group Meeting

Basic Concepts

Bring to the Peer Group Meeting written responses to each of the following. Explain your answers to each question.

  1. Define the meaning of each of the symbols that appear in Equation (1): F ⇀ E = k ⁢ q 1 ⁢ q 2 r 2 ⁢ r ^ F ⇀ E = k ⁢ q 1 ⁢ q 2 r 2 ⁢ r ^ .
  2. Clearly distinguish the meanings of source points and field points.
  3. If you reverse the choice of source point and field point in Equation (1), how does the calculated electric force change? Does Equation (1) agree or disagree with Newton's third law?
  4. Electric charges can be either positive or negative. What is the direction of the electric force in Equation (1) when both charges are positive? When both charges are negative? When one charge is positive and the other negative?
  5. Compare the basic electrical force, the Coulomb law, Equation (1), with Newton's law of Gravitation, F ⇀ G = G ⁢ m 1 ⁢ m 2 r 2 ⁢ ( - r ^ ) F ⇀ G = G ⁢ m 1 ⁢ m 2 r 2 ⁢ ( - r ^ ) . In what ways are these two fundamental forces similar? In what ways are they dissimilar?
  6. Carefully define the meaning of each of the symbols that appear in Equation (3): F ⇀ E q [ r ⇀ ] = k ⁢ q ⁢ ∑ n = 1 N q n r n 2 ⁢ r ^ n F ⇀ E q [ r ⇀ ] = k ⁢ q ⁢ ∑ n = 1 N q n r n 2 ⁢ r ^ n .
  7. State why the calculation in the case of multiple source charges involves multiple (and distinct) displacement vectors.
  8. In the worked out example, all of the charges lie in the same plane, and all the vectors involved in the solution are two-dimensional. What if not all of the charges lie in a plane, so that three-dimensional vectors are required? Would this make any difference in the statement of Equation (3)?
  9. Like all other forces, the electric force is a vector quantity, having direction as well as magnitude and units. Generally speaking, which attribute, magnitude or direction, is the more important for a vector quantity?

Preliminary Exercises

Bring your work on these exercises to the Peer Group Meeting.

  1. A hydrogen atom consists of a proton and an electron, both of which particles have both mass and electric charge. So both electric and gravitational forces act in the hydrogen atom. Are both forces attractive? Which force is larger, and how much larger? (Look up the masses and charges in your textbook.) Why is it not necessary to know the distance between the proton and electron in the hydrogen atom to answer this question?
  2. In the example of four charges on the corners of a square, assume that all of the charges have the same value q q, and the square has side a a. (a) What is the resultant electric force on the field charge? (b) Now set q 1 = q 3 = - q q 1 = q 3 = - q and make no other changes. What is now the resultant electric force on the field charge?
    Figure 1
    Figure 1 (CF3.jpg)
  3. Taking again the example of identical charges on the corners of a square, describe in a qualitative way how the force on the field charge would change if it were moved from coordinates { 0 , a } { 0 , a } to the coordinates { a 2 , a } { a 2 , a } . Assume that all the charges have the same value.
  4. Select from the end-of-chapter problems in your textbook two exercises that are straightforward applications of Equation (1), and work them out.
  5. Select from the end-of-chapter problems in your textbook two exercises that are straightforward applications of Equation (3), and work them out.
  6. Read the problems to be addressed in the Peer Group meeting, and plan strategies for solving them.

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