Teacher Notes

Investigating Electric Charge

Inquiry Lab Kit for AP® Physics 2

Materials Included In Kit

Aluminum foil sheet, 12" x 12"
Fishing line, monofilament, 1425 ft
Pith balls, 36
Plastic straws, 12
Transparent tape, 2 rolls
Wool friction pads, 12

Additional Materials Required

(for each lab group)
Balance, 0.01-g precision (may be shared)
Ruler, cm
Scissors
Support stand with ring

Safety Precautions

The materials on this lab are considered nonhazardous. Follow all laboratory safety guidelines.

Disposal

All materials may be saved and stored for future use.

Lab Hints

  • This laboratory activity can be completed in two 50-minute class periods. It is important to allow time between the Introductory Activity and the Guided-Inquiry Design and Procedure for students to discuss and design the guided-inquiry procedures. Also, all student-designed procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day.
  • Humidity can greatly affect the success of this lab and therefore the activity is more reliable in dry weather conditions. The wrapping of pith balls in aluminum foil is done to reduce the effect of humidity. It may be necessary to wash straws or other equipment with soap to remove oils.
  • If glass rods and silk, or rubber rods, are available, they can be used as an alternative material with which to charge the pith balls.

Teacher Tips

  • Students often have difficulty distinguishing between what they know because of what they have been told and what the evidence suggests. Encourage students to not make any assumptions about how charges behave and ask them to explain conclusions based on experimental results.
  • It is important that the concept of superposition is reinforced throughout. This allows students to consider more complex charge distributions later on.
  • As an extension to this activity, a charge sensor may be used in order to pursue a more quantitative experiment. Another activity would be to ask students to build an electroscope using the concepts they have learned to further establish the ideas of conservation of charge, conduction and induction.
  • In Prelab Question 4, the calculated acceleration is massive. This is due to the sheer strength of the electromagnetic interaction. Two 1-coulomb charges placed a meter away would experience 1 million tons of repulsive force between them. Lightning bolts are extremely powerful events that occur in nature and typically have 15 C of charge traveling through them. It may be helpful to give students perspective on how much a single coulomb of charge actually is by relating the unit to something with which they have familiarity.

Further Extensions

Opportunities for Inquiry
If a charge sensor is available, measure the static charge of different objects and quantitatively study the inverse square relationship of Coulomb’s law. Design a new experiment to determine the most accurate measurements.

Alignment to the Curriculum Framework for AP® Physics 2

Enduring Understandings and Essential Knowledge

Electric charge is a property of an object or system that affects its interactions with other objects or systems containing charge. (1B)
1B1: Electric charge is conserved. The net charge of a system is equal to the sum of the charges of all objects in a system.
1B2: There are only two kinds of electric charge. Neutral objects or systems contain equal quantities of positive and negative charge, with the exception of some fundamental particles that have no electric charge.

Classically, the acceleration of an object interacting with other objects can be predicted by using F=ma. (3B)
3B2: Free-body diagrams are useful tools for visualizing forces exerted on a single object and writing the equations that represent a physical situation.

At the macroscopic level, forces can be categorized as either long-range (action-at-a-distance) forces or contact forces (3C)
3C2: Electric force results from the interaction of one object that has electric charge with another object that has an electric charge.

The electric charge of a system is conserved. (5C)
5C2: The exchange of electric charges among a set of objects in a system conserves electric charge.

Learning Objectives
1B1.1: The student is able to make claims about natural phenomena based on conservation of electric charge.
1B1.2: The student is able to make predictions, using the conservation of electric charge, about the sign and relative quantity of net charge of objects or systems after various charging processes, including conservation of charge in simple circuits.
1B2.1: The student is able to construct an explanation of the two-charge model of electric charge based on evidence produced through scientific practices.
1B2.2: The student is able to make a qualitative prediction about the distribution of positive and negative electric charges within neutral systems as they undergo various processes.
1B2.3: The student is able to challenge claims that polarization of electric charge or separation of charge must result in a net charge on the object.
3B1.4: The student is able to predict the motion of an object subject to forces exerted by several objects using an application of Newton’s second law in a variety of physical situations.
3B2.1: The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively.
3C2.1: The student is able to use Coulomb’s law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interactions between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2).
3C2.2: The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces.
3C2.3: The student is able to use mathematics to describe the electric force that results from the interaction of several separated point charges (generally 2 to 4 point charges, though more are permitted in situations of high symmetry).
5C2.1: The student is able to predict electric charges on objects within a system by application of the principle of charge conservation within a system.
5C2.2: The student is able to design a plan to collect data on the electrical charging of objects and electric charge induction on neutral objects and qualitatively analyze that data.
5C2.3: The student is able to justify the selection of data relevant to an investigation of the electrical charging of objects and electric charge induction on neutral objects.

Science Practices
1.2 The student can describe representations and models of natural or man-made phenomena and systems in the domain.
1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively.
2.2 The student can apply mathematical routines to quantities that describe natural phenomena
2.3 The student can estimate numerically quantities that describe natural phenomena.
3.1 The student can pose scientific questions.
4.1 The student can justify the selection of the kind of data needed to answer a scientific question.
4.2 The student can design a plan for collecting data to answer a particular scientific question.
4.3 The student can collect data to answer a particular scientific question.
5.1 The student can analyze data to identify patterns and relationships.
5.2 The student can refine observations and measurements based on data analysis.
6.1 The student can justify claims with evidence.
6.2 The student can construct explanations of phenomena based on evidence produced through scientific practices.
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.
7.2 The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understanding and/or big ideas.

Correlation to Next Generation Science Standards (NGSS)

Science & Engineering Practices

Asking questions and defining problems
Developing and using models
Planning and carrying out investigations
Engaging in argument from evidence
Obtaining, evaluation, and communicating information

Disciplinary Core Ideas

MS-PS2.A: Forces and Motion
HS-PS2.A: Forces and Motion

Crosscutting Concepts

Patterns
Cause and effect
Systems and system models
Energy and matter

Performance Expectations

MS-PS2-5. Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact
HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

Answers to Prelab Questions

  1. Based on your understanding of gravity and Equation 1, what is the relationship between the magnitude of the electric force and distance of electrically charged objects?

    Due to the similarities in the respective equations for both types of forces, it can be inferred that electricity, like gravity, is subject to an inverse square law where the magnitude of the attraction (or repulsion) between objects varies by the square of the distance between them.

  2. In general is gravity stronger, weaker or equal in strength to the electric force?

    The force of gravity is a much weaker force.

  3. What does it mean when an object is said to be electrically neutral?

    All macroscopic objects are composed of fundamental particles such as electrons, neutrons and protons in atoms. If an object is electrically neutral, then it has the same quantity of negative charges (electrons) as positive charges (protons).

  4. Consider a 20-g marble with a charge of -2 C in the vicinity of a -5 C fixed charge on a tabletop. The smaller charge is placed 30 cm left of the fixed charge.
    1. Draw a free-body diagram of the marble.
      {14011_PreLabAnswers_Figure_1}
    2. Are the forces acting on the marble balanced? If not, what is the direction of movement?

      The forces are not balanced. The direction of movement is to the left, in the direction of the electric force.

    3. Consider the same system on a long, frictionless surface. What is the instantaneous acceleration of the marble?

      FE = (9 x 109N•m2/C2)(–2 C x –5 C)/(0.32 m) = 1 x 1012N.
      FE = ma = 0.02 kg x a
      a = 5 x 1013m/s2

    4. What is the instant acceleration if the marble is instead placed 2 m away?

      a = 1.125 x 1012 m/s2

Sample Data

Introductory Activity

  • As the experiment is performed, it is important not to let your hands or other objects touch the tape. Explain why this precaution is necessary.

    It is important to not touch the tape because coming in contact with the tape will neutralize the charge accumulated by grounding it. In other words, it will enable electron transfer.

  • Describe the interactions between two T tapes, two B tapes, and a T and B tape. Explain, in qualitative terms, the charge of the T and B tape pieces.
    {14011_Data_Table_1}
    When the tape is pulled off the tabletop it acquires charge. When two stacked pieces are pulled off the table together and then separated, electrons “flow” from one piece to the other. One piece will be negatively charged, while the other piece will be positively charged. The exact designation of which piece has the positive charge and which piece has the negative charge cannot be determined. However, it can be determined that the B tapes all have the same charge because they repel each other. The same can be said for the T tapes. The separate B and T tapes must have opposite charges because they are always observed to attract each other.
Guided-Inquiry Activity
{14011_Data_Table_2}
Analyze the Results
  • Calculate the magnitude of charge on each pith ball for every trial.

    To calculate magnitude of charge:

    {14011_Data_Equation_1}
    {14011_Data_Figure_4}
  • Calculate the quantity of excess electrons that must be on each ball.

    Divide the value of q by 1.602 x 10–19 C to get the total number of electrons.

  • How did conservation of electric charge play a role in your design?

    The principle of conservation of electric charge allowed for the assumption that each pith ball would accumulate the same quantity of charge. This is so because the pith balls are in contact with each other and the charge would be distributed equally throughout the system, causing the pith balls to repel away from each other. Without the assumption allowed by conservation of charge, the calculation could not have been done.

Answers to Questions

Guided-Inquiry Activity

  1. A glass rod is positively charged by rubbing it with wool. It is then brought near a pith ball wrapped in aluminum foil. The pith ball is initially attracted to the rod but after making contact it is quickly repelled away (see Figure 1).
    {14011_Data_Figure_1}
    1. As the pith ball is attracted to the rod, without making contact, what is the charge on the pith ball? The overall charge on the pith ball is neutral. The reason the pith ball is attracted to the rod is because there is an induced negative charge on the side closest to the rod as the electrons that are relatively free to move around are attracted to the positive rod.
    2. After contact, what is the sign of the charge on the rod and the ball? Why?

      The charge on the ball is now positive. The positive rod attracted electrons off the pith ball and onto the rod due to conduction. The rod remains positive because the pith ball does not have enough electrons to neutralize it. We know the charge on the pith ball is positive because it is repelled away from the rod.

    3. Draw a free body diagram of the pith ball after it makes contact with the rod.
      {14011_Data_Figure_2}
    4. What is the magnitude of the electric force on the 0.1-g pith ball?

      0.1 g = 0.0001 kg
      mg = FTy
      2.5/10 – sin(θ)
      θ = 14.78°
      FC =FTx, FTytan(
      θ) = FTx
      mgtan(θ) = FC = (0.0001 kg)(9.81 m/s2)tan(14.78°) = 2.59 x 10–4 N

      {14011_Data_Figure_3}
  2. A rubber rod that has been rubbed with wool is negatively charged and brought near a pith ball that has a neutral charge.
    1. Predict what would happen when the rubber rod is brought near the pith ball.

      The pith ball would be attracted to the rubber rod. The electrons in the pith ball would move away from the rod and a positive charge would be induced on the pith ball side closest to the rod, causing attraction.

    2. Describe the transfer of charge if the rubber rod makes contact with the pith ball.

      The ball would stick to the rod momentarily and then repel away after it has acquired a negative charge. Electrons from the rod would transfer to the pith ball.

  3. Two pith balls wrapped in aluminum foil hang from the ends of a string, touching. They are both charged via conduction by a rubber rod that has been rubbed with wool.
    1. Predict what the flow of electrons is when the rod is rubbed with the wool. What is the flow of electrons when the rod makes contact with the pith balls?

      Electrons flow from the wool to the rod causing it to have a net negative charge. Once in contact with the pith balls, electrons will flow from the rod to the pith balls.

    2. Is the charge on one pith ball greater than, equal to, or less than the charge on the second pith ball? Justify your reasoning using the principle of conservation of electric charge.

      Due to conservation of electric charge, while the pith balls are in contact, the electrons will disperse evenly between them. The charge on one pith ball is equal to the charge on the second pith ball.

  4. With your partner, write a detailed procedure to determine the quantity of charge on two pith balls of equal charge. Review additional variables that may affect the reproducibility or accuracy of the experiment.

    For this experiment, the pith balls should be wrapped with aluminum foil so their masses are equivalent; measure mass with a 0.01-g precision balance. Attach a ball to the end of a piece of fishing line and have that line hung at a point where each pith ball hangs at the same height. The length of the fishing line should be measured. Once the pith ball apparatus is set up, charge the plastic straw by rubbing it with wool for a short duration and bring the straw in contact with both pith balls. After the pith balls are charged, measure the distance of the pith balls from each other. Using mass, the length of the string, and the distance between pith balls, the charge on each pith ball can be determined using algebraic and trigonometric methods.

Review Questions for AP® Physics 2
  1. Coulomb’s law allows for the calculation of the electric force between two point charges. Consider the figure below.
    {14011_Answers_Figure_1}
    A student made this statement regarding the system:

    “According to Coulomb’s law, the force due to the –Q charge is negative and the force due to the +Q charge is positive. Therefore, the forces cancel each other out and the net electric force on the –q charge is zero.”

    1. Do you agree with this statement? Explain.

      No. The positive charge attracts the negative charge in the middle and the negative charge repels it. The net force is not zero and is instead in the direction of the +Q charge.

    2. How can Coulomb’s law be applied in situations where there are more than two point charges?

      One can use Coulomb’s law for different combinations of pairs of charges and use superposition to accurately determine the net force. Superposition allows one to deduct the direction of the net force by adding all force vectors directly influencing the system.

  2. Rank, in increasing magnitude, the four charge configurations below according to the magnitude of the net electric force on charge +q. Explain why you made your selections.
    {14011_Answers_Figure_2}
    The rank in order of magnitude of the net electric force on charge +q is B,A,C,D. Figure B has the most net force on charge +q because the –2 Q and +2 Q charges attract and repel, respectively, the +q in the same direction. This is more charge than is disposable in any other configuration. Figure D has a net force of zero on charge +q because the 45° angles of the bottom charges cause the vertical and horizontal components of force to be equal, meaning that vertically the force from the bottom charges is due to +Q charge and horizontally they cancel. The +Q charge above cancels out the force from the +Q total charge made up of the vertical components of the bottom charges. This leaves figures A and C. Figure A must have more net force on charge +q because the +3Q of charge inducing a force on the charge is concentrated directly below, whereas in figure C the +3Q is spread out over a curved path beneath it, and superposition of the vectors of force from the left and right +Q charges would cause a smaller net force on charge +q than in figure A.
  3. Consider the following situation.
    {14011_Answers_Figure_6}
    1. If the system is at equilibrium, what is the ratio of the magnitude of charge of +Q to –Q?

      The repulsive force on the +q from +?Q is equal to the attractive force on +q by the –Q charges combined. So:
      2(–Q)cos(θ) = +Q, (+Q) = 1.6383(–Q)

    2. If +Q = 10 C, what is the value of charge on the –Q charges?

      10/1.6383 = 6.1039 C
      Derive an equation that represents the electric force on charge +q. The distance of the –Q charge from the +q charge is s.

      {14011_Answers_Equation_1}

References

AP® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

Student Pages

Investigating Electric Charge

Inquiry Lab Kit for AP® Physics 2

Introduction

The notion that opposite charges attract and like charges repel is commonly known, but what is the intrinsic property behind these interactions? How are these charges accumulated? Discover how the transfer of electrons across materials provides observable electric forces.

Concepts

  • Electric charge
  • Conservation of charge
  • Forces
  • Conduction and induction
  • Coulomb’s law

Background

Electric charge is an intrinsic property of matter carried by fundamental particles such as electrons and quarks. In the late 18th century, French physicist Charles-Augustin de Coulomb (1736–1806) measured the manner by which the force between electrically charged objects were related to distance. He found that, like gravity, the electric force obeys an inverse square law (Equation 1).

{14011_Background_Equation_1}
where

k = Coulomb’s constant,
q = charge,
r = distance between the charges.

This is known as Coulomb’s law. Coulomb’s constant is equivalent to 1/4πε0 (roughly 9 x 109N•m2/C2), where ε0 is the permeability of free space. In 1911, American physicist Robert Millikan (1868–1953) quantified the charge of an electron as –1.602 × 10–19 coulombs. This is the elementary charge. There are both negative and positive charges, with the proton having a charge of 1.602 x 10–19 C. Like mass and energy, charge cannot be created or destroyed. Therefore, charge is conserved, and this principle is referred to as the conservation of electric charge.

When certain materials are rubbed together, a transfer of electrons can occur between them, leaving one object positively charged (via a loss of electrons) and the other negatively charged (via a gain of electrons). A neutral object can become charged via conduction; that is, if a negatively charged object is brought into contact with the neutral object, electrons will flow and both will be left with a net negative charge.

Induction is another manner in which charges can be accumulated. If a negatively charged rod is brought near (but not touching) a metal sphere, the electrons in that sphere will be repelled and the side of the sphere closest to the negative rod will have an accumulation of positive charge. However, the sphere still has a net neutral charge. If the metal sphere is grounded (the Earth can accept or supply an “unlimited” number of electrons), then the electrons in the sphere have a path to follow. Therefore, the rod repels electrons into the Earth, and if the ground connection is then removed before the rod is moved from the vicinity of the sphere, the sphere will be left with a net positive charge.

Experiment Overview

The purpose of this advanced inquiry investigation is to derive and understand the relationship between the magnitude of the electric force and distance in a system of two charged objects. An introductory activity is performed in order to analyze the transference of electrostatic charges and to infer the existence of two kinds of charge. Then, an apparatus designed to enable a semiquantitative exploration of Coulomb’s law will be studied.

Materials

Aluminum foil
Fishing line
Pith balls
Plastic straws
Ruler, cm
Support stand with ring
Tape, transparent, matte finish
Wool friction pads

Prelab Questions

  1. Based on your understanding of gravity and Equation 1, what is the relationship between the magnitude of the electric force and distance of electrically charged objects?
  2. Is gravity stronger, weaker or equal in strength to the electric force?
  3. What does it mean when an object is said to be electrically neutral?
  4. Consider a 20-g marble with a charge of –2 C in the vicinity of a –5 C fixed charge on a tabletop. The smaller charge is placed 30 cm to the left of the fixed charge.
    1. Draw a free-body diagram of the marble.
    2. Are the forces acting on the marble balanced? If not, what is the direction of movement?
    3. Consider the same system on a long, frictionless surface. What is the instant acceleration of the marble?
    4. What is the instantaneous acceleration if the marble is instead placed 2 m away?

Safety Precautions

The materials in this lab are considered nonhazardous. Follow all laboratory safety guidelines.

Procedure

Introductory Activity

  1. Tear off a 12-cm piece of tape.
  2. Make “handles” by folding each end of the tape to form portions that are not sticky.
  3. Firmly press the sticky side down on a desk or tabletop (preferably unpainted).
  4. Smooth the piece of tape down so the entire length is firmly pressed on the work surface.
  5. Peel the tape off and hang from edge of the work surface, being careful to only touch the handle. Observe the behavior of the tape as objects are brought toward it (e.g., a ruler, a hand).
  6. Repeat steps 1– 4 for a second piece of tape.
  7. Peel the second piece of tape off and bring the non-sticky sides of both tape pieces towards each other. Record your observations.
  8. Repeat steps 1– 4 for two new pieces of tape.
  9. Once both pieces of tape are pressed onto the work surface, write “B” (for bottom) on the handle of each.
  10. Then press a second piece of tape on top of each “B” tape and write “T” (for top) on each piece.
  11. Quickly pull the stack of tape pieces off the table and then separate the T and B tapes from each other.
  12. Hang one B and one T tape from the edge of your work surface.
  13. Repeat step 11 with the other stack of tape pieces and bring the B and T tapes one at a time near each of the hanging tapes. Observe and record what happens as different combinations are tested.
Analyze the Results
  • As the experiment is performed, it is important not to let hands or other objects touch the adhesive surface of the tape. Explain why this precaution is necessary.
  • Describe the interactions between two T tapes, two B tapes, and a T and B tape. Explain, in qualitative terms, the charge of the T and B tape pieces.
Guided-Inquiry Design and Procedure
Form a working group with other students to discuss the following questions.
  1. A glass rod is positively charged by rubbing it with wool. It is then brought near a pith ball wrapped in aluminum foil. The pith ball is initially attracted to the rod but after making contact it is quickly repelled away (see Figure 1).
    {14011_Procedure_Figure_1}
    1. As the pith ball is attracted to the rod, without making contact, what is the charge on the pith ball?
    2. After contact, what is the sign of the charge on the rod and the pith ball? Why?
    3. Draw a free body diagram of the pith ball after it makes contact with the rod.
    4. What is the magnitude of the electric force on the 0.1-g pith ball?
  2. A rubber rod that has been rubbed with wool is negatively charged and brought near a pith ball that has a neutral charge.
    1. Predict what would happen when the rubber rod is brought near the pith ball.
    2. Describe the transfer of charge if the rubber rod makes contact with the pith ball.
  3. Two pith balls wrapped in aluminum foil hang from the ends of a string, touching. They are both charged via conduction by a rubber rod that has been rubbed with wool.
    1. Predict what the flow of electrons is when the rod is rubbed with the wool. What is the flow of electrons when the rod makes contact with the pith balls?
    2. Is the charge on one pith ball greater than, equal to, or less than the charge on the second pith ball? Justify your reasoning using the principle of conservation of electric charge.
  4. With your partner, write a detailed procedure to determine the quantity of charge on two pith balls of equal charge. Review additional variables that may affect the reproducibility or accuracy of the experiment.
  5. Carry out your experiment and record multiple trials for different angles or distances measured.
Analyze the Results 
  • Calculate the magnitude of charge on each pith ball for every trial.
  • Calculate the quantity of excess electrons that must be on each ball.
  • How did conservation of electric charge play a role in your design?

Student Worksheet PDF

14011_Student1.pdf

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