Chapter 20: Electric Potential and Electric Potential Energy

20-1 Electric Potential Energy and the Electric Potential

Electric potential energy arises from the conservative nature of the electric force. It takes work to move a charge in an electric field, and this work is related to changes in potential energy.

• Electric Force: A conservative force, meaning it has an associated potential energy.

• Work and Potential Energy: The change in potential energy is the negative of the work done by the electric force.

• Electric Potential (V): Defined as the potential energy per unit charge. SI unit: joule/coulomb = volt (V).

• Electron Volt: A unit of energy, defined as the energy gained by an electron moving through a potential difference of 1 volt.

• Relation to Electric Field: The electric field is related to the rate of change of electric potential.

Key Equations:

• Change in potential energy:

• Electric potential:

• Electron volt:

• Relation between electric field and potential:

20-2 Energy Conservation

Energy conservation applies to electric forces just as it does to other conservative forces. The total energy (kinetic plus potential) remains constant for a charge moving in an electric field.

• Conservation Principle: For a mass or charge moving from point A to B, the total energy is conserved.

• Charge Acceleration: Positive charges accelerate toward decreasing electric potential; negative charges accelerate toward increasing electric potential.

• Potential Energy: Both types of charges move to regions of lower potential energy.

Key Equations:

• Total energy:

• For electric force:

20-3 The Electric Potential of Point Charges

The electric potential due to a point charge can be calculated, and the total potential from multiple charges is the sum of individual potentials.

• Potential Difference: The difference in potential energy between two points A and B.

• Electric Potential of a Point Charge: , where is Coulomb's constant, is the charge, and is the distance from the charge.

• Multiple Charges: The total electric potential is the algebraic sum of the potentials from each charge.

Key Equations:

• Potential difference:

• Point charge potential:

• Total potential:

20-4 Equipotential Surfaces and the Electric Field

Equipotential surfaces are regions where the electric potential is constant. The electric field is always perpendicular to these surfaces and is strongest where the surfaces are closest together.

• Equipotential Surfaces: Surfaces (or lines in 2D) of constant electric potential.

• Relationship: The electric field is perpendicular to equipotential surfaces.

• Conductors: Ideal conductors are equipotential surfaces; more curved conductors have larger electric fields.

• Applications: Electric fields and potential differences exist in the human body, measured by devices like electrocardiographs and electroencephalographs.

20-5 Capacitors and Dielectrics

Capacitors store electric charge and energy. Their capacitance depends on the geometry and the presence of a dielectric material, which increases capacitance by reducing the electric field.

• Capacitor: Two conducting plates separated by a distance.

• Capacitance: Relates charge to potential difference. SI unit: farad (F).

• Parallel-Plate Capacitor: Capacitance given by , where is plate area, is separation, and is the permittivity of free space.

• Dielectric: An insulator placed between plates increases capacitance by reducing the potential difference for the same charge.

• Dielectric Constant (): Property of the material; capacitance becomes .

• Dielectric Breakdown: If the electric field exceeds the dielectric strength, the material becomes conductive.

Key Equations:

• Capacitance:

• Parallel-plate capacitance:

• With dielectric:

Example Table: Dielectric Constants

Example Table: Dielectric Strengths

20-6 Electrical Energy Storage

Capacitors store electrical energy, which can be used in various applications. The energy stored depends on the charge and potential difference.

• Energy Storage: The energy stored in a capacitor is given by .

• Applications: Used in camera flashes, cardiac defibrillators, and many electronic devices.

• Energy Density: Energy per unit volume in an electric field: .

Key Equations:

• Energy stored:

• Energy density:

Summary of Chapter 20

• Electric force is conservative and has associated potential energy.

• Electric potential is defined as potential energy per unit charge.

• Relation between electric field and potential:

• Energy conservation applies to electric forces.

• Positive charges accelerate toward decreasing potential; negative charges toward increasing potential.

• Electric potential of a point charge:

• Equipotential surfaces are perpendicular to electric fields.

• Capacitors store charge and energy; capacitance depends on geometry and dielectrics.

• Dielectric breakdown occurs at high electric fields.

• Energy stored in capacitors is used in many devices.