Physics of light and optics by Justin Peatross; Michael Ware

By Justin Peatross; Michael Ware

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C (c) Show that the displacement current in the gap leads to the identical magnetic field when using surface S 2 . Solution: (a) We’ll assume that the cross-sectional area of the wire A is much wider than the gap separation. 10) reduces to E A since there is essentially no field other than in the gap. 10) integrates to Q/ 0 , and the electric field turns out to be E = Q/( 0 A). (b) Let the contour C be a circle at radius r . The magnetic field points around the circumference with constant strength.

10 It indicates that a changing electric field behaves like a current in the sense that it produces magnetic fields. 4) is apparent. No doubt this played a part in motivating Maxwell’s work. In summary, in the previous section we saw that the basic physics in Ampere’s law is present in the Biot-Savart law. 23) yields the corrected form of Ampere’s law. 9 Although Gauss developed his law in 1835, it was not published until after his death in 1867, well after Maxwell published his laws of electromagnetism, so in practice Maxwell accomplished much more than merely fixing Ampere’s law.

P = 0), the polarization can often be written as function of the electric field: P = 0 χ (E ) E, where χ (E ) = χ1 + χ2 E + χ3 E 2 · · · . e. ) are typically small, so only the first term is important at low intensities. The field of nonlinear optics deals with intense light-matter interactions, where the higher order terms of the expansion become important. This can lead to phenomena such as harmonic generation. Starting with Maxwell’s equations, derive the wave equation for nonlinear optics in an isotropic medium: ∇2 E − µ0 0 1 + χ1 ∂2 E = µ0 ∂t 2 ∂2 χ2 E + χ3 E 2 + · · · E 0 ∂t 2 + µ0 ∂J ∂t We retain the possibility of current here since, for example, in a gas some of the molecules might ionize in the presence of a strong field, giving rise to currents.

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