In a region of vacuum with no charges and no currents

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic waves and their propagation · Electromagnetic waves and their propagation

Electricity, Magnetism and Electromagnetism, Ch Plane electromagnetic waves: polarisation, energy flux and radiation pressure

Problem

In a region of vacuum with no charges and no currents, a plane wave travels along +x+x with magnetic field B=B0cos⁡(kx−ωt)z^\mathbf{B} = B_0\cos(kx - \omega t)\hat{\mathbf{z}}, where B0=12 nTB_0 = 12\ \mathrm{nT} and the frequency is f=1.50 GHzf = 1.50\ \mathrm{GHz}. There the Maxwell equation ∇×B=μ0ε0 ∂E/∂t\nabla\times\mathbf{B} = \mu_0\varepsilon_0\,\partial\mathbf{E}/\partial t holds, whose yy component reads −∂Bz/∂x=μ0ε0 ∂Ey/∂t-\partial B_z/\partial x = \mu_0\varepsilon_0\,\partial E_y/\partial t. Take ε0=8.854×10−12 F m−1\varepsilon_0 = 8.854\times10^{-12}\ \mathrm{F\,m^{-1}} and μ0=4π×10−7 T m A−1\mu_0 = 4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}. ((a)) Compute 1/μ0ε01/\sqrt{\mu_0\varepsilon_0} and hence the wavelength and wave number of this wave. ((b)) Integrate the component equation above to obtain Ey(x,t)E_y(x,t), and give its amplitude E0E_0 and the direction of E\mathbf{E}. ((c)) Find the intensity of the wave.

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