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The E-field vector and the dipole vector define a plane, and the torque is directed normal to that plane with the direction given by the right-hand rule. A dipole in such a uniform field may twist and oscillate, but receives no overall net force with no linear acceleration of the dipole. The dipole twists to align with the external field.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. Electric polarization of a given dielectric material sample is defined as the quotient of electric dipole moment (a vector quantity, expressed as coulombs*meters (C*m) in SI units) to volume (meters ...
The force of one magnetic dipole on another is determined by using the magnetic field of the first dipole given above and determining the force due to the magnetic field on the second dipole using the force equation given above. Using vector notation, the force of a magnetic dipole m 1 on the magnetic dipole m 2 is: (,,) = [() + + () ()] where ...
r is the vector from the position of the dipole to the position where the field is being measured r is the absolute value of r: the distance from the dipole r̂ = r / r is the unit vector parallel to r; m is the (vector) dipole moment μ 0 is the permeability of free space
Due to the changing current, there is a time dependent magnetic field which induces an electric field. Due to the shape, the field appears as if it were a dipole. Electric field around the current loop. It shows a dipole shape and the polarity difference can be seen above and below the loop as the current direction changes with time.
In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations.It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field.
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