Electricity and Magnetism · Problem 9.26

ELECTRIC FIELDS IN MATTER — Edward Purcell & David Morin

Physics — E&M · em-waves

Problem

Here is a particular electromagnetic field in free space: Ex=0,Ey=E0sin⁡(kx+ωt),Ez=0;(9.64)E_x = 0, \quad E_y = E_0\sin(kx+\omega t), \quad E_z = 0;\tag{9.64} Bx=0,By=0,Bz=−(E0/c)sin⁡(kx+ωt).B_x = 0, \quad B_y = 0, \quad B_z = -(E_0/c)\sin(kx+\omega t). (a) Show that this field can satisfy Maxwell's equations if ω\omega and kk are related in a certain way. (b) Suppose ω=1010\omega = 10^{10} s−1^{-1} and E0=1E_0 = 1 kV/m. What is the wavelength? What is the energy density in joules per cubic meter, averaged over a large region? From this calculate the power density, the energy flow in joules per square meter per second.

Related theory

Browse the problem library