electric displacement field

(noun)

A vector field that appears in Maxwell's equations.

Related Terms

Examples of electric displacement field in the following topics:

  • Gauss's Law

    • Gauss's law is a law relating the distribution of electric charge to the resulting electric field.
    • Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
    • In words, Gauss's law states that: The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.
    • Each of these forms in turn can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge.

  • Maxwell's Equations

    • Fundamentally, they describe how electric charges and currents create electric and magnetic fields, and how they affect each other.
    • Gauss's law relates an electric field to the charge(s) that create(s) it.
    • Faraday's law describes how a time-varying magnetic field (or flux) induces an electric field.
    • Maxwell added a second source of magnetic fields in his correction: a changing electric field (or flux), which would induce a magnetic field even in the absence of an electrical current.
    • He named the changing electric field "displacement current."

  • Polarization

    • The concept of polarity is very broad and can be applied to molecules, light, and electric fields.
    • A dielectric is an insulator that can be polarized by an electric field, meaning that it is a material in which charge does not flow freely, but in the presence of an electric field it can shift its charge distribution.
    • If an electric field is applied to an atom, the electrons in the atom will migrate away from the applied field.
    • When a dipolar molecule is exposed to an electric field, the molecule will align itself with the field, with the positive end towards the electric field and the negative end away from it.
    • When an electric field (E) is applied, electrons drift away from the field.

  • Dipole Moments

    • Fundamentally, for the case of point charges with values +q and -q, an electric dipole moment (p) can be defined as the vector product of the charges and the displacement vector d:
    • The displacement vector is the vector with a magnitude equal to the distance between the charges and a direction pointing from the negative charge to the positive charge.
    • All dipoles will experience a torsional force, or torque, when they are placed in external electric fields.
    • This torque rotates the dipole to align it with the field.
    • Torque (τ) can be calculated as the cross product of the electric dipole moment and the electric field (E), assuming that E is spatially uniform:

  • Solving Problems with Vectors and Coulomb's Law

    • To address the electrostatic forces among electrically charged particles, first consider two particles with electric charges q and Q , separated in empty space by a distance r.
    • Suppose that we want to find the electric force vector on charge q.
    • Electric Force on a Field Charge Due to Fixed Source Charges
    • Since we can have only one origin of coordinates, no more than one of the source points can lie at the origin, and the displacements from different source points to the field point differ.
    • The displacements of the field charge from each source charge are shown as light blue arrows.

  • Electric Flux

    • Electric flux is the rate of flow of the electric field through a given area.
    • Electric flux is the rate of flow of the electric field through a given area (see ).
    • If the electric field is uniform, the electric flux passing through a surface of vector area S is $\Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta$ where E is the magnitude of the electric field (having units of V/m), S is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to S.
    • For a non-uniform electric field, the electric flux dΦE through a small surface area dS is given by $d\Phi_E = \mathbf{E} \cdot d\mathbf{S}$ (the electric field, E, multiplied by the component of area perpendicular to the field).
    • The red arrows for the electric field lines.

  • The Production of Electromagnetic Waves

    • Electromagnetic waves are the combination of electric and magnetic field waves produced by moving charges.
    • As it travels through space it behaves like a wave, and has an oscillating electric field component and an oscillating magnetic field.
    • Once in motion, the electric and magnetic fields created by a charged particle are self-perpetuating—time-dependent changes in one field (electric or magnetic) produce the other.
    • This means that an electric field that oscillates as a function of time will produce a magnetic field, and a magnetic field that changes as a function of time will produce an electric field.
    • Notice that the electric and magnetic field waves are in phase.

  • Introduction to Simple Harmonic Motion

    • You will remember from your elementary physics courses that if you want to know the electric field produced by a collection of point charges, you can figure this out by adding the field produced by each charge individually (my treatment of elementary simple harmonic motion is standard in most introductory physics textbooks.
    • That is, if we have n charges $\left\{q_i\right\}_{i=1,n}$, then the total electric field is (neglecting constant factors):
    • is the electric field of the ith point charge (Coulomb's law).
    • This property, whereby we can analyze a complicated system (in this case the total electric field $\mathbf{E}(q_1 + q_2 + \cdots q_n)$) by breaking it into its constituent pieces (in this case $\mathbf{E}(q_i)$) and then adding up the results is known as linearity.
    • So for small displacements, the equation for the pendulum is:

  • Electric vs. Magnetic Forces

    • Where F is the force vector, q is the charge, and E is the electric field vector.
    • It should be emphasized that the electric force F acts parallel to the electric field E.
    • A consequence of this is that the electric field may do work and a charge in a pure electric field will follow the tangent of an electric field line.
    • The angle dependence of the magnetic field also causes charged particles to move perpendicular to the magnetic field lines in a circular or helical fashion, while a particle in an electric field will move in a straight line along an electric field line.
    • The electric field is directed tangent to the field lines.

  • Electric Field from a Point Charge

    • A point charge creates an electric field that can be calculated using Coulomb's law.
    • The electric field of a point charge is, like any electric field, a vector field that represents the effect that the point charge has on other charges around it.
    • Let's first take a look at the definition of the electric field of a point particle:
    • The electric field of a point charge is defined in radial coordinates.
    • The electric field of a point charge is symmetric with respect to the θdirection.