Electric potential

DURACELL Electric Potential

Introduction to Electrical Potential and Energy

• Electrical Potential Energy (PEE): Stored energy based on the position of charge.

• Potential Energy Definition:

  • Stored Energy (Energy of Position).

  • Gravitational Potential Energy Formula:
    $PE_g = mgh$

  • Electrical Potential Energy Formula:
    $PEE = qEr$

  • Where:

    • $PEE$ = Electrical Potential Energy (Joules)

    • $q$ = Test charge (Coulombs)

    • $E$ = Electric Field Strength (Newtons per Coulomb)

    • $r$ = Displacement of charge from reference point (meters)

    • Displacement can also be represented as $\Delta r$ , $\Delta x$ , or $\Delta d$

• Work Against Nature: If work is done against nature, the potential energy increases.

Examples involving Electrical Potential Energy

Example 1

• Context: An electron at rest on Earth, midpoint between parallel plates, 10 cm apart.

  • a) Electrical potential energy at point P: To be calculated based on given conditions.

  • b) Electron is moved 3 cm higher: Determine the change in electrical potential energy.

  • c) Analyze whether the electrical potential energy increased or decreased.

  • d) Release of the electron: Determine its speed upon reaching the positive plate (neglecting gravity).

  • e) Effects of switching the electron with a proton on the previous answers.

Example 2

• Point Charge Context:

  • Formula:
    $PEE = qEr$ and $PEE=q(\frac{kQ}{r^2})r$

  • Simplified to:
    $PEE=\frac{kqQ}{r}$

• Problem: Calculate electrical potential energy between an electron and a proton in a hydrogen atom with a diameter of $1\cdot10^{-9}{ m}$ .

Electric Potential

• Definition of Electric Potential (V):

  • It is the change in electrical energy per unit charge:
    $V=\frac{W}{q}$

  • Where:

    • $V$ = Electric Potential (volts)

    • $W$ = Work or electrical energy (Joules)

    • $q$ = Charge (Coulombs)

  • Note: Work is the change in energy.

Example 3

• Context: Work done on a proton:

  • Problem Statement: Calculate electric potential when $4.8\cdot10^{-19}J$ of work is performed.

Electrical Potential Definitions and Concepts

• Electric Potential: Change in electrical energy per unit charge.

• Potential Difference: The change in electric potential from one point to another.

• Voltage: The potential energy difference across a component.

• Potential Drop: The voltage decreased across a resistor.

• Electromotive Force (EMF): Another term for voltage.

  • Similarities: All of the above terms imply nearly the same concept.

Relations for Parallel Plates

• For parallel plates and any uniform electric field:

  • $V=\frac{W}{q}$

  • $V=\frac{qEd}{q}$

  • Final form for parallel plates:
    $V = Ed$

Additional Examples involving Potential Difference

Example in Electric Fields

• An electron starts at rest at a point P, situated 5 cm above a negative plate:

  • a) Calculate the potential difference when the electron is moved 3 cm higher.

  • b) Calculate the potential difference if moved 3 cm to the right from that position.

  • c) Determine the potential difference between the plates separated by 10 cm.

Voltage Specifications

• Measured Voltages for various sources:

  • AAA Battery: 1.5 V

  • AA Battery: 1.5 V

  • C Battery: 1.5 V

  • D Battery: 1.5 V

  • Phone Battery: 3.8 V

  • Nine Volt Battery: 9 V

  • Car Battery: 12 V

  • Wall Outlet: 120 V

Point Charge and Equipotential Lines

• For point charges:

  • Electric Potential Formula:
    $V=\frac{W}{q}$ , $V=\frac{kQ}{r}$

• Equipotential Lines: Lines that represent equal voltages in an electric field (e.g. 3V, 2V, 1V).

Additional Point Charge Example

• Scenario: A 4.2 microcoulomb sphere and hydrogen nucleus 30 cm apart:

  • a) Calculate the electrostatic force between both charges.

  • b) Determine electric field strength at the location of the nucleus.

  • c) Calculate the electric potential energy at that point.

  • d) Determine the electric potential at that point.

  • e) Calculate the acceleration of the proton placed in the given field.