Lecture 2: Potential and Capacitance

Stored Energy and Potential

• Energy is stored when charges are separated, creating a potential difference measured in volts.
• A capacitor is a practical example of this principle.

Potential Energy

• Separating positive and negative charges stores energy.
• This is because if released, the charges will move together, generating kinetic energy, thus demonstrating stored potential energy.
• Photosynthesis uses this process: light separates charges, which then recombine to generate biologically useful energy.

Quantifying Potential Energy

• Separating charges requires work, calculated by force exerted over distance.
• The force between charges is described by Coulomb's law.
• The potential energy U between two charges is given by: U = k \frac{qQ}{r} where:
  • k is Coulomb's constant.
  • q and Q are the magnitudes of the charges.
  • r is the distance between the charges.
• Potential energy is measured in joules.

Electric Potential

• Electric potential (or potential) is the energy per unit charge.
• For an isolated charge, the electric potential V is: V = k \frac{q}{r} where:
  • k is Coulomb's constant.
  • q is the magnitude of the charge.
  • r is the distance from the charge.
• Potential is measured in volts, where 1 volt = 1 joule/coulomb.
• Electric potential fills the space around a charge.

Equipotentials

• Equipotentials are lines or surfaces where the electric potential is constant.
• Moving a charge along an equipotential requires no work because there is no potential difference.

Relationship Between Electric Fields and Potentials

• Electric fields and potentials are related.
• The electric field is always perpendicular to equipotential surfaces.
• The electric field is the negative rate of change of potential with distance: E = -\frac{dV}{dz} where:
  • E is the electric field.
  • V is the electric potential.
  • z is the direction perpendicular to the equipotential surface (the direction of the steepest change in potential).

Visualizing Fields and Potentials

• Electric field lines show the direction of force on a positive charge.
• Potential can be visualized as a height map, where higher