Prove that Faraday’s law is covariant under Lorentz Transformation.
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Prove that Faraday’s law is covariant under Lorentz Transformation.
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- 4. Derive the maxwell equations for U, H, G and A Table 6.2.1: Maxwell Relations Function U H A G Differential dU = TdS-pdV dH = TdS + Vdp dA=-pdV - SdT dG = Vdp - SdT Natural Variables S, V S, P V, T P, T Maxwell Relation (or)--( др as V (37), = (35), as (OP), - (OV), = V (3r), - - (35), = TIn quantum interpretation of the electromagnetic waves in vacuum the photon has the energy E = hw/2n and the momentump= hk/2n. So the ratio E of the energy to the momentum is = c, the speed of light in k vacuum. Similar relation can be obtained in classical electrodynamics as follows. Consider the time-averaged energy density of the electromagnetic field ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a wave S = E × H and confirm that its ratio to the time-averaged energy density ratio is equal to the speed of light in vacuum, S/e = c.10. The wave equation for electromagnetic waves in frame S is given by a²E(x,t) 1 a²E(x,t) = 0. Use the Lorenz coordinate transformation c2 at2 and find the wave equation in frame S' that moves with the velocity of u with respect to S.