Chapter 7: Electric Potential

INTRODUCTION

• CHAPTER 7: Electric Potential
    - Topics Covered:
      - 7.1 Electric Potential Energy
      - 7.2 Electric Potential and Potential Difference
      - 7.3 Calculations of Electric Potential
      - 7.4 Determining Field from Potential
      - 7.5 Equipotential Surfaces and Conductors
      - 7.6 Applications of Electrostatics

• Discussion on electrical phenomena, highlighting the significance of electrical energy (stored in batteries, transmitted via power lines, etc.) and voltage.

• Example applications include:
    - Energy storage in batteries
    - Electric potential in lightning strikes

• Distinction made between energy (measured in joules) and voltage (measured in volts). Different applications may involve different scales of voltage (e.g., motorcycle vs. car batteries).

7.1 Electric Potential Energy

LEARNING OBJECTIVES

• By the end of this section, you will be able to:
    - Define the work done by an electric force.
    - Define electric potential energy.
    - Apply work and potential energy in systems with electric charges.

Key Concepts

• Electric potential energy is analogous to gravitational potential energy. The motion of a positive charge in an electric field is like an object moving in a gravitational field.

• Work Done: The work done on a charge by the electric field can be understood through an analogy to gravitational force.

• Coulomb Force: The electrostatic (Coulomb) force is conservative, allowing for the definition of electric potential energy associated with charge configuration.

Example: Kinetic Energy of a Charged Particle

• A charge Q is accelerated by Coulomb forces:
    - Work done as it moves from a distance of 10 cm (r1) to 15 cm (r2) is calculated.
    - If Q starts from rest:
      - $W = ext{change in kinetic energy} = ext{potential energy loss} = - rac{k imes q_1 imes q_2}{r_2} + rac{k imes q_1 imes q_2}{r_1}$

Comparison with Gravitational Potential Energy

• Gravitational potential energy and electric potential energy behave similarly due to the work done being path-independent (though the actual forces are different).

• In spherical coordinates:
    - $U = - rac{kq_1q_2}{r}$, where k is Coulomb's law constant.

7.2 Electric Potential and Potential Difference

LEARNING OBJECTIVES

• You will be able to:
    - Define electric potential, voltage, and potential difference.
    - Define the electron-volt.
    - Calculate electric potential and potential difference from potential energy and electric field.

Key Concepts

• Electric Potential (V): Defined as the potential energy per unit charge, where voltage is the difference in potential energy for a charge moved between two points.
    - $V = rac{U}{q}$

• Potential Difference: The change in potential energy as a charge moves from one point to another in an electric field, measured in volts (V).
    - $ext{Voltage} = rac{U_f - U_i}{q}$

• Electron-Volt (eV): Energy given to a charge when accelerated through a potential difference of 1 V, equivalent to $1 ext{ eV} = 1.602 imes 10^{-19} ext{ J}$.

7.3 Calculations of Electric Potential

LEARNING OBJECTIVES

• You will be able to:
    - Calculate the potential due to a point charge.
    - Calculate the potential of a system of multiple point charges.
    - Describe an electric dipole.

Key Concepts

• The electric potential due to a point charge is given by:
    - $V = rac{k imes q}{r}$, where r is the distance from the charge.

• Superposition of Potentials: The total potential from multiple point charges is the algebraic sum of individual potentials:
    - $V_{ ext{total}} = V_1 + V_2 + … + V_n$

• Electric Dipole: Consists of two equal and opposite charges separated by a distance d, with a dipole moment defined as:
    - $ext{Dipole Moment} <br>ightarrow p = q imes d$.

Example Problems

• Assessing potentials and energies involving dipoles and point charges, using integrations when necessary.

7.4 Determining Field from Potential

LEARNING OBJECTIVES

• You will be able to:
    - Explain how to calculate the electric field in a system from the given potential.

Key Concepts

• The electric field can be derived from potential through the gradient:
    - $E = -<br>abla V$

• Directional relationship: The electric field points in the direction of decreasing potential.

Example Problems

• Calculate electric fields from given potential functions using calculus.

7.5 Equipotential Surfaces and Conductors

LEARNING OBJECTIVES

• You will be able to:
    - Define equipotential surfaces and equipotential lines.
    - Explain the relationship between equipotential lines and electric field lines.

Key Concepts

• Equipotential Surfaces: Surfaces on which the potential is constant; thus, no work is needed to move charges along these surfaces.

• Relationship with electric fields: Equipotential surfaces are perpendicular to electric field lines at every point.

Example Problems

• Graphing equipotential lines, calculating distances between surfaces, and comparing conductive surfaces to equipotential lines.

7.6 Applications of Electrostatics

LEARNING OBJECTIVES

• You will be able to:
    - Describe some of the many practical applications of electrostatics,

Case Studies

Van de Graaff Generator

• Used to create high voltage static electricity, demonstrating nuclear physics principles.

Xerography

• Electrostatic process for copying images; utilizes the properties of photoconducting materials.

Laser Printers & Ink Jet Printers

• Both making use of electrostatic principles to produce high-fidelity images.

Electrostatic Precipitators

• Remove airborne particles through charge manipulation techniques.

Key Terms and Equations

Key Terms:

• Electric dipole, electric potential, electric potential difference, electric potential energy, electron-volt, equipotential line/surface, grounding, xerography.

Key Equations:

• $U = k rac{q_1 q_2}{r}$

• $V = k rac{q}{r}$

• $E = - <br>abla V$

Summary of Key Concepts:

• Understanding electric fields and potentials provides insight into how electric forces function in various situations: from atomic interactions to macroscopic applications.