Capacitance

Parallel plate capacitors store electric charge between two conducting plates. The plates are separated by a distance, and the space between them is either a vacuum or an insulating material called a dielectric. Capacitors are used in many ways, from reducing static in radio reception to storing energy in heart defibrillators.

When the two conductors are identical parallel plates, the device is called a parallel plate capacitor. If a battery is connected to an initially uncharged capacitor,...

A spherical capacitor uses two concentric conducting spherical shells. The inner shell has radius R1, and the outer shell has radius R2. The shells carry equal and opposite charges, +Q and −Q.

For an isolated conducting spherical capacitor, the outer shell can be treated as if it were at infinity. By symmetry, the electric field between the shells points radially outward. Using Gauss’s law on a spherical Gaussian surface of radius r gives the field magnitude between the shells.

That electric...

Capacitor networks combine charge and voltage in different ways, depending on how the capacitors are connected. When several capacitors act together, they can be treated as one equivalent capacitor. The total capacitance depends on the capacitance of each capacitor and on the connection type.

In a series connection, the capacitors are connected one after another. The negative terminal of the first capacitor connects to the positive terminal of the second. When this series group is connected to...

Capacitor networks can be arranged in series or parallel, and the connection type changes how charge and voltage are shared. When the network is connected to a battery, the potential drop across each capacitor and the charge stored in each one depend on that arrangement. The full network can then be replaced by one equivalent capacitor that stores the same charge for the same potential difference.

To find the net capacitance, a capacitor network is grouped into series and parallel parts. A...

A charged capacitor stores electric potential energy by doing work during charging. This idea is similar to an archer pulling back a bowstring and storing elastic potential energy. When the arrow is released, that stored energy becomes motion. In the same way, the work put into a capacitor is stored as electric potential energy.

For a parallel plate capacitor, the process starts when it is connected to a battery. The plate attached to the negative side of the battery gains extra electrons.

Capacitors store electric potential energy, and that energy can be released over a short time. This makes them useful in a range of applications. Benjamin Franklin coined the word battery in 1749 for a series of capacitors connected to store energy.

One common use is capacitor-discharge ignition, or CDI, in small engines. In a CDI system, the energy from a capacitor ignites an induction coil, which then fires the spark plug. To find the energy stored in a typical CDI capacitor, at least two of...

A dielectric can help a parallel plate capacitor store more charge. In a basic capacitor, two conducting plates are separated by a set distance. Keeping the plates parallel can be mechanically difficult, especially when the plates are large and cannot touch each other.

A dielectric is a non-conducting material with no free or loosely bound electrons. Placing this material between the plates creates a small gap and helps hold the plates together. It also increases the capacitor’s capacitance,...

Dielectrics change the electric field, voltage, and capacitance in a capacitor. A dielectric is an insulating material placed between the plates. Its presence affects how the field behaves inside the capacitor.

Dielectrics are usually described as polar or nonpolar. In a polar dielectric, positive and negative charges are already separated, so each molecule has a permanent dipole moment. In a nonpolar dielectric, that charge separation is not present until an external electric field acts on...

Dielectric effects on electric fields explain how an insulating material changes the field between capacitor plates. When a polar dielectric is placed in an external field, its dipoles line up with the field. The opposite charges on nearby dipoles cancel each other, so the dielectric as a whole remains neutral.

When the dielectric is inserted between the plates of a capacitor, bound charges appear near the edges of the dielectric and at the metal surface. These induced surface charges create...

Polarized dielectrics form when charges inside atoms or molecules shift slightly in an electric field. A neutral atom has a positive nucleus and a negative electron cloud. An external electric field pulls them in opposite directions. The pull is balanced by the attraction between the nucleus and electrons, so the atom becomes polarized.

Some molecules, such as water, already have separated positive and negative sides. In a uniform electric field, the forces on those sides cancel. Even so, a...

Dielectric polarization explains how a material responds to an external electric field. When a dielectric is placed in the field, its charges shift so the material becomes polarized. The charge density in the dielectric is the sum of bound and free charge densities, and the total charge density can also be written in terms of the total electric field.

The bound charge density can be measured using polarization. This leads to a link between electric displacement and polarization. For linear...

Field behavior at dielectric interfaces changes when an electric field crosses from one homogeneous medium into another. That change creates a discontinuity, or sudden jump, in the field. The boundary conditions depend on which materials meet at the interface.

When the two sides are different dielectric materials, the electric field and the electric displacement are linked through the material’s permittivity. Replacing the electric field with the electric displacement in the boundary...