19.1 Electric Potential Energy: Potential Difference
- Electric potential is potential energy per unit charge.
- The potential difference between points A and B, , defined to be the change in potential energy of a charge moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol
- An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
- Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, This sum is a constant.
19.2 Electric Potential in a Uniform Electric Field
- The voltage between points A and B is where is the distance from A to B, or the distance between the plates.
- In equation form, the general relationship between voltage and electric field is where is the distance over which the change in potential, , takes place. The minus sign tells us that points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope) of the electric potential.
19.3 Electrical Potential Due to a Point Charge
- Electric potential of a point charge is .
- Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.
19.4 Equipotential Lines
- An equipotential line is a line along which the electric potential is constant.
- An equipotential surface is a three-dimensional version of equipotential lines.
- Equipotential lines are always perpendicular to electric field lines.
- The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding.
19.5 Capacitors and Dielectrics
- A capacitor is a device used to store charge.
- The amount of charge a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
- The capacitance is the amount of charge stored per volt, or
- The capacitance of a parallel plate capacitor is , when the plates are separated by air or free space. is called the permittivity of free space.
- A parallel plate capacitor with a dielectric between its plates has a capacitance given by where is the dielectric constant of the material.
- The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.
19.6 Capacitors in Series and Parallel
- Total capacitance in series
- Total capacitance in parallel
- If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.
19.7 Energy Stored in Capacitors
- Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy.
- The energy stored in a capacitor can be expressed in three ways: where is the charge, is the voltage, and is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.