Electromagnetic Waves

The figure shows a capacitor made of two circular plates each of radius $12 \mathrm{cm}$, and separated by $5 \mathrm{cm}$. The capacitor is being charged by an external source. The charging current is constant and is equal to $0.15 \mathrm{A}$, obtain the displacement current across the plates?

Some scientists have already predicted that a global nuclear war on the earth would be followed by a severe ‘nuclear winter’ with a bad effect on life on earth. What might be the basis of this prediction?

If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?

The small ozone layer on top of the stratosphere is crucial for human survival. Why?

Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the earth. Why?

It is necessary to use satellites for long distance TV transmission. Why?

Answer the following question: Long distance radio broadcasts use short - wave bands. Why? 

Given here is some famous number associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which it belongs,$14.4 \mathrm{keV}$ [energy of a particular transition in ${}^{\text{57}}\text{Fe}$ nucleus associated with a famous high-resolution spectroscopic method (Mossbauer spectroscopy)]. 
 

Given here are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs, $5890\mathrm{}\mathrm{\AA }\mathrm{}-\mathrm{}5896\mathrm{}\mathrm{\AA }$ [double lines of sodium].

Given here is a famous number associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which it belongs, $1057 \mathrm{MHz}$ (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).

Suppose that the electric field part of an electromagnetic wave in vacuum is $\mathbf{E}=\left\{\right(3.1 \mathrm{N}/\mathrm{C}) \mathrm{c}\mathrm{o}\mathrm{s} [(1.8 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{m}) \mathrm{y}+(5.4\times {10}^6 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}) \mathrm{t}\left]\right\} \hat{\mathbf{i}}$. Write an expression for the magnetic field part of the wave.

Suppose that the electric field part of an electromagnetic wave in vacuum is $\mathrm{E}=\left\{\right(3.1 \mathrm{N}/\mathrm{C}) \mathrm{c}\mathrm{o}\mathrm{s} [(1.8 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{m}) \mathrm{y}+(5.4\times {10}^6 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}) \mathrm{t}\left]\right\} \hat{\mathbf{i}}$. What is the amplitude of the magnetic field part of the wave? Take, $c = 3\times {10}^8 \mathrm{m}/\mathrm{s}$

Suppose that the electric field part of an electromagnetic wave in vacuum is $\mathbf{E}=\left\{\right(3.1 \mathrm{N}/\mathrm{C}) \mathrm{c}\mathrm{o}\mathrm{s} [(1.8 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{m}) \mathrm{y}+(5.4\times {10}^6 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}) \mathrm{t}\left]\right\} \hat{\mathbf{i}}$. What is the frequency $\nu$ ?

Suppose that the electric field part of an electromagnetic wave in vacuum is$\mathbf{E}=\left\{\right(3.1\mathrm{N}/\mathrm{C}\left)\mathrm{c}\mathrm{o}\mathrm{s}\right[(1.8\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{m})\mathrm{y}+(5.4\times {10}^6\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s})\mathrm{t}\left]\right\}\widehat{\mathbf{i}}$. What is the wavelength?

Suppose that the electric field part of an electromagnetic wave in vacuum is $E=\left\{\right(3.1 \mathrm{N}/\mathrm{C}\left)\mathrm{c}\mathrm{o}\mathrm{s}\right[(1.8 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{m})\mathrm{y}+(5.4\times {10}^6 \mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s})\mathrm{t}\left]\right\} \hat{\mathrm{i}}$ .What is the direction of propagation?

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $2.0\times {10}^{10}\mathrm{Hz}$ and amplitude $48\mathrm{V}{\mathrm{m}}^{-1}$. Show that the average energy density of the $\mathrm{E}$ field equals the average energy density of the $\mathrm{B}$ field. $\left[\mathrm{c}=3\times {10}^8\mathrm{m}{\mathrm{s}}^{-1}\right]$

Suppose that the electric field amplitude of an electromagnetic wave is $E_0=120\hspace{0.17em}\mathrm{N}/\mathrm{C}$ and that its frequency is $\mathrm{\nu }=50.0 \mathrm{M}\mathrm{H}\mathrm{z}.$ Determine, $B_{0, }\omega ,\hspace{0.17em}k,$ and $\mathrm{\lambda }.$ Find expressions for $E$ and $B$.

The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $B_0=510\hspace{0.17em}\mathrm{nT}.$ What is the amplitude of the electric field part of the wave?

A charged particle oscillates about its mean equilibrium position with a frequency of ${\mathrm{10}}^{\mathrm{9}}\hspace{0.17em}\mathrm{Hz}$. What is the frequency of the electromagnetic waves produced by the oscillator?

A radio can tune in to any station in the $7.5 \mathrm{MHz}$ to $12 \mathrm{MHz}$ bands. What is the corresponding wavelength band? Take, $c = 3\times {10}^8 \mathrm{m}/\mathrm{s}$