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?

(II) An 18.5-mW laser puts out a narrow beam 2.40 mm in diameter. What are the rms values of E and B in the beam?

Light is emitted from an incandescent lightbulb filament in wave-train bursts about 10^-8 s in duration. What is the length in space of such wave trains?

The electric field of a plane EM wave is given by $E_x=E_0\cos (kz+\omega t),E_y=E_z=0$. Determine (a) the direction of propagation and (b) the magnitude and direction of $\overrightarrow{B}$.

Suppose that a right-moving EM wave overlaps with a left-moving EM wave so that, in a certain region of space, the total electric field in the y direction and magnetic field in the z direction are given by $E_y=E_0\sin (kx-\omega t)+E_0\sin (kx+\omega t)$ and $B_z=B_0\sin (kx-\omega t)-B_0\sin (kx+\omega t)$. Find the mathematical expression that represents the standing electric and magnetic waves in the y and z directions, respectively.

The oscillator of a 98.3-MHz FM station has an inductance of 2.8 μH. What value must the capacitance be?

If the magnetic field in a traveling EM wave has a peak magnitude of 16.5 nT, what is the peak magnitude of the electric field?