Thermodynamics, 5th Edition

(5.6.15)

where (r,t) represents the electric field vector in its dependence on position r and time t and c represents the velocity of light. Casual inspection verifies that the solution to the wave equation is given by

${ℰ}_x={ℰ}_{0x}\sin (\omega t)\cos (k_{x}x)\sin (k_{y}y)\sin (k_{z}z)$ (5.6.16a)

(5.6.16a)

${ℰ}_y={ℰ}_{0y}\sin (\omega t)\sin (k_{x}x)\cos (k_{y}y)\sin (k_{z}z)$ (5.6.16b)

(5.6.16b)

${ℰ}_z={ℰ}_0$