where p =BS= flux density(in gauss)x area S. The time-changing flux, dap/dt, can happen as a result of 1. A changing magnetic field within a stationary circuit 2. A circuit moving through a 3. A combination of 1 and 2 The electrical circuit may have n turns and ther emf =-N We can write emf=E. dL and in the presence of changing magnetic fields or a moving electrical circuit E.dL no longer required to be equal to 0 as it was for stationary fields and circuits. Maxwell's Equations Because the flux d can be written JB. ds we have emf=E dl=-d/dt B. ds, and by using Stokes'theorer (V×E)·ds=-dB/dtds V×E=-dB/dt That is, a spatially changing electric field produces a time-changing magnetic field. This is one of Maxwells equations linking electric and magnetic fields By a similar argument it can be shown that V×H=J+dDdt This is another of Maxwells equations and shows a spatially changing magnetic field produces a time-changing electric field. The latter dD/dt can be treated as an electric current which flows through a dielectric, e.g., in a capacitor, when an alternating potential is applied across the plates. This current is called the displacement current to distinguish it from the conduction current which flows in conductors. The conduction current involves the movement of electrons from one electrode to the other through the conductor (usually a metal). The displacement current involves no translation of electrons or holes but rather an alternating polarization through out the dielectric material which is between the plates of the capacitor From the last two equations we see a key conclusion of Maxwell: that in electromagnetic fields a time-varying magnetic field produces a spatially varying electric field and a time-varying electric field produces a spatially varying magnetic field. Maxwell's equations in point form, then, are V×E=dB/dt V×H=J+dD/d These equations are supported by the following auxiliary equations: D=EE (displacement permittivity x electric field intensity) B= uh (flux density permeability x magnetic field intensity) e 2000 by CRC Press LLC© 2000 by CRC Press LLC where F = BS = flux density (in gauss) ¥ area S. The time-changing flux, dF/dt, can happen as a result of 1. A changing magnetic field within a stationary circuit 2. A circuit moving through a steady magnetic field 3. A combination of 1 and 2 The electrical circuit may have N turns and then We can write emf = E · dL and in the presence of changing magnetic fields or a moving electrical circuit E · dL is no longer required to be equal to 0 as it was for stationary fields and circuits. Maxwell’s Equations Because the flux F can be written eB · ds we have emf = E · dL = –d/dt B · ds, and by using Stokes’ theorem (— 2 E) · ds = –dB/dt ds or — 2 E = –dB/dt That is, a spatially changing electric field produces a time-changing magnetic field. This is one of Maxwell’s equations linking electric and magnetic fields. By a similar argument it can be shown that — 2 H = J + dD/dt This is another of Maxwell’s equations and shows a spatially changing magnetic field produces a time-changing electric field. The latter dD/dt can be treated as an electric current which flows through a dielectric, e.g., in a capacitor, when an alternating potential is applied across the plates. This current is called the displacement current to distinguish it from the conduction current which flows in conductors. The conduction current involves the movement of electrons from one electrode to the other through the conductor (usually a metal). The displacement current involves no translation of electrons or holes but rather an alternating polarization through￾out the dielectric material which is between the plates of the capacitor. From the last two equations we see a key conclusion of Maxwell: that in electromagnetic fields a time-varying magnetic field produces a spatially varying electric field and a time-varying electric field produces a spatially varying magnetic field. Maxwell’s equations in point form, then, are — 2 E = dB/dt — 2 H = J + dD/dt — · D = rv — · B = 0 These equations are supported by the following auxiliary equations: D = eE (displacement = permittivity 2 electric field intensity) B = mH (flux density = permeability 2 magnetic field intensity) emf d d = -N t F