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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.
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 ...
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 nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied ...
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.
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 ...
Poynting vector in a static field, where E is the electric field, H the magnetic field, and S the Poynting vector. The consideration of the Poynting vector in static fields shows the relativistic nature of the Maxwell equations and allows a better understanding of the magnetic component of the Lorentz force, q(v × B).
This equation says, in effect, that the flux lines of D must begin and end on the free charges. In contrast ρ b {\displaystyle \rho _{\text{b}}} , which is called the bound charge, is an effective density of the charges that are part of a dipole .