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)
Support stand with ring
The materials on this lab are considered nonhazardous. Follow all laboratory safety guidelines.
All materials may be saved and stored for future use.
- 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.
- 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.
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.
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.
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
Cause and effect
Systems and system models
Energy and matter
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
- 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.
- In general is gravity stronger, weaker or equal in strength to the electric force?
The force of gravity is a much weaker force.
- 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).
- 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.
- Draw a free-body diagram of the marble.
- 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.
- 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
- What is the instant acceleration if the marble is instead placed 2 m away?
a = 1.125 x 1012 m/s2
Analyze the Results
- Calculate the magnitude of charge on each pith ball for every trial.
To calculate magnitude of charge:
- 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
Review Questions for AP® Physics 2
- 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).
- 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.
- 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.
- Draw a free body diagram of the pith ball after it makes contact with the rod.
- 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
- A rubber rod that has been rubbed with wool is negatively charged and brought near a pith ball that has a neutral charge.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Coulomb’s law allows for the calculation of the electric force between two point charges. Consider the figure below.
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.”
- 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.
- 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.
- 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.
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.
- Consider the following situation.
- 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)
- 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.
AP® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.