Chapter 17: Electrical Potential and Electric Energy; 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.
• Calculate 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.
• 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.
• Calculate 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.
• 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:

• Block Scheduling
  Electric energy, electrical potential energy difference, potential difference, and equipotential surfaces need two half blocks. Stress the relationship between potential and work and energy. Capacitance, dielectrics, and energy stored in a capacitor require one blocks.

Key Words:

potential, p. 503 electric potential, p. 503 electrical potential difference, p. 503 volt (V), p. 503 voltage, p. 503 electrical potential, p. 506 equipotential surface, p. 507 equipotential lines, p. 507 electron volt, p. 508 electric dipole, p. 511

polar molecules, p. 512 capacitor, p. p. 513 capacitance, p. 513 farad (F), p. 513 dielectric, p. 514 dielectric constant, p. 514 energy density, p. 517 cathode, p. 518 anode, p. 518 cathode-ray tube, p. 518

Critical Thinking Questions:

1. An electrical charge q creates a field of 4500 N/C at a point R away from the charge. The potential at that point is +1800 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. Calculate the area of a set of parallel plates 2 mm apart that would have a capacitance of 1.0 F in air.
4. A parallel plate capacitor having an area of 120 cm² and a plate gap of 0.05 mm is filled with an organic fluid and then charged from a 24 V power source. The source is disconnected and the fluid is drained off. The final voltage is 320 V.
1. What is the dielectric constant of the organic fluid?
2. Calculate the field between the plates if the capacitor is filled with a light oil having a dielectric of 5.2.
5. A proton is released from rest from the positive plate in a parallel plate capacitor maintained in vacuum. The plates are 1.00 mm apart and are connected to a 24.0 V battery.
1. What force does the proton experience?
2. What is the acceleration?
3. With what velocity does the proton impact the positive plate?
4. How long does it take the proton to travel to the positive plate?
5. What is the kinetic energy of the proton 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 where electrical potential is used to calculate the work done in transporting a charge through the field.
• Stress that electrical potential is a property of space while potential energy is a property assigned to a charge.
• Student may have difficulty recognizing that potential difference and difference in potential energy is not the same quantity.
• 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 with an example.