Lesson Plans

Physics 4th Edition ©2002

by Jerry Wilson and Anthony Buffa

Week 18

Chapter 16: Electrical Potential, Energy, and Capacitance

College Board Performance Objectives:

• Distinguish by definition and example between potential energy, electric potential, and electric potential difference.
• Distinguish between positive and negative work.
• Compute the potential energy of a known charge at a given distance from another known charge and state whether the potential energy is positive or negative.
• Determine the electric potential at any point due to a charge of known magnitude.
• Compute the electric potential at a point in the neighborhood of a number of isolated charges.
• Find the force that would be exerted on a given charge placed between two oppositely charged parallel plates of known separation and potential difference.
• Describe and illustrate Millikan's Oil-Drop Experiment and its significance in the history of the development of physics.
• Define the electron volt, eV, and be able to express energy in terms of this unit.
• Define the dielectric strength of a material and describe the part it plays in limiting the charge that can be placed on a conductor.
• Discuss the effects of the size and the shape of a conductor on its ability to store a charge.
• Derive a relationship between applied voltage, capacitance, and total charge.
• Find the capacitance of a parallel-plate capacitor when the area of the plates is given and they are separated by a medium of a known dielectric constant.
• Define permittivity and give examples illustrating its effect on a capacitor.
• Calculate the equivalent capacitance of a number of capacitors arranged in (1) series, (2) parallel, and (3) series and parallel combination.
• Define and calculate the energy of a charged capacitor.

College Board Lab Objectives:

• Devise an experiment to measure the charge on an electron.
• Experimentally determine charge and voltage relationships for capacitors in series, parallel, and combined networks.

Suggested Labs:

• Charge on an Electron
• Equipotentials and Electric Fields
• Capacitance

Resources:

• Student Edition — pp. 551–537
• Student Study Guide — pp. 202–215
• Instructor's Solution Manual — pp. 205–216
• Test Items File — pp. 276–286

Pacing Guide:

• Electrical Energy in the Electrostatic Field—day 1
• Electrical Potential Energy Difference—days 1 and 2
• Potential Difference—day 2
• Equipotential Surfaces and the Electric Field—day 2
• Capacitance—day 3
• Dielectrics—day 3
• The Permittivity of Space—day 3
• Equivalent Capacitance—days 3 and 4
• The Energy of a Charged Capacitor—day 4
• Lab—day 5
• Block Scheduling
  Electrical energy, electrical potential energy difference, potential difference, and equipotential surfaces need a single block. Stress the relationship between potential and work and energy. Capacitance, dielectrics, equivalent capacitance, and energy stored in a capacitor require two blocks.

Key Words:

Critical Thinking Questions:

1. An electrical charge q creates a field of 5400 N/C at a point R away from the charge. The potential at that point is +2700 V. Determine values of q and R.
2. Calculate the radius of a spherical capacitor that will have a capacitance of 1.0 F in air.
3. The potential difference between two parallel plates 4.0 cm apart is 2000 V. A silk thread holding a 10 mg body attached to the upper edge of the positive plate makes an angle of 5° with the plate. What is the magnitude of the charge on the body?
4. A 24.0 µF capacitor and a 12.0 µF capacitor are connected in series to a 60 V source. Calculate the charge and voltage on each. The capacitors are disconnected from the power source and reconnected in parallel. What is the new charge and voltage on each?
5. An electron is released from rest from the negative plate in a parallel plate capacitor maintained in vacuum. The plates are 2.00 mm apart and are connected to a 12.0 V battery.
   1. What force does the electron experience?
   2. What is the acceleration?
   3. With what velocity does the electron impact the positive plate?
   4. How long does it take the electron to travel to the positive plate?
   5. What is the kinetic energy of the electron on impact?
   6. How much work does the electrical field do?

Troubleshooting Tips/Error Traps:

• Students may treat the electric potential as a vector. Stress the definition of electrical potential. Emphasize that electrical fields have two properties. The electric field is a vector with magnitude and direction, and electrical potential is a scalar with magnitude only. Electric field is used to calculate the force on a charged particle at a given point in space whereas electrical potential is used to calculate the work done in transporting a charge through the field.
• Stress that potential is a property of space while potential energy is a property assigned to a charge.
• Students may have difficulty understanding that the surface of a conductor is an equipotential surface. Stress the definition of the equipotential surface.
• Students have difficulty understanding that potential is zero at great distance from a charge. Emphasize the concept with appropriate examples.
• Students may have difficulty recognizing that potential difference and difference in potential energy is not the same quantity.

End of Chapter Activity:

1. A proton and an electron are 1.0 cm apart in air. Show the direction of the electrical field in the region around the charges and indicate the equipotential surfaces.
2. Research the Millikan Oil-Drop Experiment.
3. Research the Van de Graaff generator.
4. If the net charge of a capacitor is always zero, what is stored in the capacitor?

Suggested Problem Assignments: