Voltage, Electric Energy, and Capacitors Summary

Electric Potential Energy and Capacitance

Defibrillators and Capacitors

  • Defibrillators use capacitors to store electrical energy and deliver a controlled electric shock to the heart.

  • The shock stops irregular heart contractions, allowing the heart to restart with a normal rhythm.

  • A capacitor consists of two parallel conductive plates with opposite charges and an electric field between them.

Electric Potential Energy

  • Electric potential energy: Energy a charged object has when held in an electric field.

  • Work is performed when a force is applied over a distance.

  • The change in potential energy equals the work done by an external force or the negative work done by the electric force.

Electric Potential

  • Electric potential: Electric potential energy difference per unit charge.

  • Voltage: Electric potential difference.

  • Voltage = -Electric\ Field \times Distance

  • Units of electric potential are joules per coulombs, or volts.

Equipotential Lines

  • Equipotential lines: Lines along which all test charges have the same voltage; they are perpendicular to the electric field.

  • In a capacitor, these lines run parallel to the plates.

Electric Potential of a Point Charge

  • The electric potential created by a point charge is the difference in potential energy per unit charge between a spot right next to the point charge and somewhere infinitely far away.

  • Electric potential generated by a point charge: V = k \frac{q}{r}, where k is Coulomb's constant, q is the charge, and r is the distance from the charge.

  • For an electric dipole (one positive and one negative point charge), the electric potentials from individual charges can be added together.

Capacitance

  • Capacitance (C): Measure of how much charge a capacitor can store. C = \frac{Q}{V}, where Q is the charge and V is the voltage.

  • Units of capacitance are farads (F), where 1 farad = 1 coulomb per volt.

  • Capacitance is determined by the size and shape of the capacitor: C = \epsilon0 \frac{A}{d}, where A is the area of each plate, d is the distance between them, and \epsilon0 is the permittivity of free space.

Dielectrics

  • Dielectric: Insulating material (like plastic or glass) used to increase capacitance by preventing charge from jumping between plates.

  • The full equation for capacitance with a dielectric is C = k \epsilon_0 \frac{A}{d}, where k is the dielectric constant.

Energy Storage

  • Potential energy stored in a capacitor: U = \frac{1}{2} QV.

  • Energy density: Amount of energy stored in the electric field per unit volume. u = \frac{1}{2} \epsilon_0 E^2 , where E is the electric field.