32. Electromagnetic Waves

Electromagnetic waves produced byX-raymachines typically haveafrequencyof approximately$3.5\times10^{16}Hz$ .What is the wave numberof thesewaves?

The magnetic field of a travelling electromagnetic wave is described by the wave function $B\left(z,t\right)=1.0\times10^{-3}\sin\left(kz-1.27\times10^{12}t\right)$, where k is the wave number. Write the complete wave function for the electric field of this wave.

The magnetic field of an electromagnetic wave in a vacuum is $B_z=\left(3.0\mu T\right)\sin \left[\right(1.00\times {10}^7)x-\omega t]$, where x is in m and t is in s. What are the wave's wavelength?

The electric field of an electromagnetic wave in a vacuum is $E_y=\left(20.0\text{ V/m}\right)\cos \left[\right(6.28\times {10}^8)x-\omega t]$, where x is in m and t is in s. What are the wave's magnetic field amplitude?

(III) (a) When a circular parallel-plate capacitor is being charged as in Example 31–1, show that the Poynting vector $\overrightarrow{S}$ points radially inward toward the center of the capacitor, parallel to the plates.

(II) A spherically spreading EM wave comes from a 2100-W source. At a distance of 5.0 m, what is the intensity, and what is the rms value of the electric field?