Name: bound charges in polarized dielectrics
Uploaded: 2025-05-22T09:06:00.000Z
Duration: 1 min 29 s
Channel: JoVE

When a dielectric is placed in an electric field, the dipoles align along the field direction. This effect is called polarization, which is the dipole moment per unit volume.
Consider a long string of aligned dipoles with uniform dipole moments. The equal and opposite charges in adjacent dipoles cancel each other, leaving net negative and positive charges at the dielectric surface, called surface-bound charges.
The surface-bound charge density is the charge per unit area. Using the definition of the dipole moment, the charge can be expressed in terms of polarization.
For an oblique surface, this charge is distributed over an extended area. Defining a normal to this area gives the expression for surface-bound charge density.
When the polarization is non-uniform, the alignment of dipoles accumulates charges inside the dielectric, leading to volume-bound charges that are equal and opposite to the surface-bound charges.
The potential created by a polarized dielectric at a field point can be estimated solely from these bound charges and is the sum of the potentials produced by the surface and volume-bound charges.

potential due to a polarized object

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water, inherently have this separation. For such molecules, when kept in a uniform electric field, the forces exerted on the positive and negative sides cancel each other; however, a net torque exists. In both cases, the dipoles point along the electric field direction, leading to polarization, which is given by the dipole moment per unit volume. 
Consider a cylindrical dielectric material. In a string of aligned dipoles along the length of the cylinder, with a constant dipole moment, the equal and opposite charges in the adjacent dipoles cancel each other. Hence, there are net charges at both ends of the cylinder called surface-bound charges. These are called bound charges as they are still bound to the specific atoms or molecules and are not free to move in the dielectric. The surface-bound charge density is the charge per unit area on either surface. 
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Suppose the electric field and polarization are diverging in nature. In that case, the alignment of the dipoles accumulates charges inside the polarized dielectric, leading to volume-bound charges that are equal and opposite to the surface-bound charges.
<img alt="Truss static equilibrium, ΣFx=0, ΣFy=0, ΣM=0, structural stability diagram using joint forces." src="/files/ftp_upload/14183/14183_Equation_2.png" style="text-align: center; height: 28px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram, equations ΣFx=0, MA=0, illustrating physics principles.">
Recalling the potential due to a dipole, the potential created by the polarized dielectric at any field point can be measured by knowing the potentials due to these surface-bound and volume-bound charges. 
<img alt="Static equilibrium; ΣFx=0 and ΣFy=0; diagram illustrates balance of forces on object." src="/files/ftp_upload/14183/14183_Equation_3.png" style="text-align: center; height:52px;" data-altupdatedat="1754904545000" data-alt="n-hexane (C6H14) structural formula diagram, organic chemistry molecular structure analysis.">

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the ...

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bound charges in polarized dielectrics

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 net torque acts on the molecule. In both cases, the dipoles point along the electric field direction, and the material becomes polarized. Polarization is the dipole moment per unit volume.

A cylindrical dielectric can show this effect clearly. If dipoles align along the length of the cylinder, the opposite charges in neighboring dipoles cancel. This leaves net charge at both ends of the cylinder. These end charges are called surface-bound charges. They are bound to the atoms or molecules and cannot move freely through the dielectric. The surface-bound charge density is the charge per unit area on a surface.

If the electric field and polarization diverge, the dipoles can also create charge inside the material. This produces volume-bound charges, which are equal and opposite to the surface-bound charges. The potential due to the polarized dielectric at any field point can then be found from the potentials of the surface-bound and volume-bound charges. The result follows the same idea as the potential due to a dipole.

Bound Charges in Polarized Dielectrics

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Learn how polarization creates surface-bound and volume-bound charges in dielectrics, and how these charges determine the potential in polarized materials.

Bound Charges in Polarized Dielectrics | JoVE K12

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Bound Charges in Polarized Dielectrics

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