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: $C = \epsilon<em>0 \frac{A}{d}$, where $A$ is the area of each plate, $d$ is the distance between them, and $\epsilon</em>0$ 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.