Electric potential and electric potential energy are key concepts in understanding how charges interact in electric fields. These quantities help us analyze the energy stored in electrical systems and the work required to move charges.

Practical applications of these concepts are found in batteries, capacitors, and particle accelerators. The electron volt unit is particularly useful for describing energy in atomic and subatomic processes, connecting the microscopic world to everyday electrical phenomena.

Electric Potential and Electric Potential Energy

Electric potential vs potential energy

• Electric potential (voltage) scalar quantity measured in volts (V) represents the potential difference between two points in an electric field measures the work required to move a positive test charge from one point to another
• Electric potential energy scalar quantity measured in joules (J) energy stored in a system due to the configuration of charges depends on the electric potential difference and the charge quantity

Potential difference and energy relationship

• Relationship: $\Delta PE = q \Delta V$
  • $\Delta PE$: Change in electric potential energy (J)
  • $q$: Charge quantity (C)
  • $\Delta V$: Potential difference (V)
• Practical scenarios
  • Batteries provide a potential difference that can power devices (flashlights) higher voltage batteries can provide more energy to a given charge
  • Capacitors store electric potential energy in an electric field between two conducting plates (electronic circuits) potential difference across the plates determines the stored energy
• Equipotential surfaces are regions where the electric potential is constant, and no work is done when moving charges along these surfaces

Electron volt in atomic processes

• Electron volt (eV) unit of energy equal to the work done to move an electron through a potential difference of 1 volt conversion: 1 eV = $1.602 \times 10^{-19}$ J
• Applications in atomic and subatomic processes
  • Measuring binding energies of electrons in atoms different energy levels correspond to specific electron volt values (hydrogen atom)
  • Describing the energy of photons photon energy $E = hf$ can be expressed in electron volts (X-rays)
  • Characterizing particle accelerators accelerator energies are often expressed in mega-electron volts (MeV) or giga-electron volts (GeV) (Large Hadron Collider)

Calculations with potential difference

• Formula: $\Delta PE = q \Delta V$
  • $\Delta PE$: Change in electric potential energy (J)
  • $q$: Charge quantity (C)
  • $\Delta V$: Potential difference (V)
• Steps to solve problems
  1. Identify the given quantities (charge and potential difference)
  2. Determine the unknown quantity (change in electric potential energy)
  3. Substitute the known values into the formula
  4. Perform the calculation and report the result with appropriate units

Energy and Work in Electric Fields

• Electric fields are created by electric charges and exert forces on other charges
• Work done by the electrostatic force when moving a charge in an electric field changes the charge's electric potential energy
• The principle of conservation of energy applies to the conversion between kinetic and potential energy in electric fields