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During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. This eddy current is formed by the movement of the wheels. So, by Lenz's law, the magnetic field formed by the eddy current will oppose its cause. Thus the wheel will face a force opposing the initial movement of the ...
Substituting the earlier solution for the constant W we find: = (/) = that is, the power given by integrating the Poynting vector over a cross section of the coaxial cable is exactly equal to the product of voltage and current as one would have computed for the power delivered using basic laws of electricity.
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
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.
Some observed electromagnetic phenomena cannot be explained with Maxwell's equations if the source of the electromagnetic fields are the classical distributions of charge and current. These include photon–photon scattering and many other phenomena related to photons or virtual photons , " nonclassical light " and quantum entanglement of ...
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
Faraday's law of induction (or simply Faraday's law) is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction , is the fundamental operating principle of transformers , inductors , and many types of electric ...
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]