The energy density (energy per unit volume) associated with an electromagnetic wave propagating in vaccum of free space is \(\mathrm{u}=\frac{1}{2} \varepsilon_{o} E^{2}+\frac{1}{2 \mu_{o}} B^{2}. \text { where, } \frac{1}{2} \varepsilon_{o} E^{2}=\mathrm{u}_{\mathrm-{E}}\) is the energy density in an electric field and \(\frac{1}{2 \mu_{o}} B^{2}=u_{B}\) is the energy density in a magnetic field. Since \(\mathrm{E}=\mathrm{Bc} \Rightarrow \mathrm{u}_{\mathrm{B}}=\mathrm{u}_{\mathrm{E}}\) The energy density of the electromagnetic wave is \(\mathrm{u}=\varepsilon_{o} E^{2}=\frac{1}{\mu_{0}} B^{2}\).

(i) Faraday's law of electromagnetic induction. This law relates electric field with the changing magnetic flux which is mathematically written as 
\(\oint \vec{E} \cdot d \vec{l}=-\frac{d}{d t} \Phi_{B}\)  (Faraday's law)
(ii) Where \(\vec{E} \) is the electric field. This equation implies that the line integral of the electric field around any close path is equal to the rate of change of magnetic flux through the closed path bounded by the surface.

Intensity of electromagnetic waves is the energy crossing per unit area pre unit time and perpendicular to the direction of propagation of electromagnetic waves.

(a) 10⁹ Hz - Radiowaves
Application: For radio & television communication.
(b) 10¹¹ Hz - microwaves
Application: used in Radar for aircraft navigation, (microwave oven for cooking).

(i) u - v rays
(ii) X - rays
(iii) ૪ - rays.

(a) X - rays are used as diagnostic tool in medicine. X-rays are used extensively in studying structures of inner atomic electron shells and crystal structures. It is used in detecting fractures, diseased organs, formation of bones and stones, observing the progress of healing bones. Further, in a finished metal product, it is used to detect faults, cracks, flaws and holes.
(b) Radio are produced by oscillators in electric circuits. It obeys reflection and diffraction. It is used in radio and communication system and cellphones.

Expression for Ampere circuital law
\(\oint { \overrightarrow { B } .\overrightarrow { dl } } ={ \mu }_{ 0 }{ I }_{ c }+{ \mu }_{ 0 }\varepsilon _{ 0 }\frac { d{ \phi }_{ E } }{ dt } \)
\(\oint { \overrightarrow { B } .\overrightarrow { dl } } ={ \mu }_{ 0 }{ (I }_{ c }+{ I }_{ d })\)
(i) In case of steady current in a conducting wire, the electric field does not change with time, condition current I_c exists but I_d may be zero
so \(\oint { \overrightarrow { B } .\overrightarrow { dl } } ={ \mu }_{ 0 }.{ I }_{ c }.\)
(ii) In the large region of space, no condition current (I_c) but there is only displacement current (I_d) to time-varying electric field (i.e. flux).
so \(\oint { \overrightarrow { B } .\overrightarrow { dl } } ={ \mu }_{ 0 }\varepsilon _{ 0 }\frac { d{ \phi }_{ E } }{ dt } \)

During charging, the electric flux between the plates capacitor keeps on changing. This results in the production of displacement current between the plates.
\({ I }_{ d }=\varepsilon _{ 0 }\left( \frac { d{ \phi }_{ E } }{ dt } \right) \)

On decreasing the frequency, reactance \({ X }_{ c }=\frac { 1 }{ \omega C } \) will increase which will lead to decrease in condition current. In this case I_d = I_c hence displacement current will decrease.

Conduction current Ie = Displacement current ID
\({ I }_{ C }={ I }_{ s }=\frac { dq }{ dt } =\frac { d }{ dt } ({ q }_{ 0 }cos2\pi \gamma t)\)
\(=-2\pi { q }_{ 0 }\gamma sin2\pi \gamma t\)

(i) It is produced by transitions of atomic nuclei and decay of certain elementary particles. They produce chemical reactions on photographic plates, fluorescence, ionization, diffraction.
(ii) Gamma rays provide information about the structure of atomic nuclei. It is used in radiotherapy for the treatment of cancer and tumor, in the food industry to kill pathogenic microorganisms.

It is produced by Sun, arc, and ionized gases. The wavelength range is 6 x 10^-10m to 4 x 10^-7m and the frequency range is 5 x 10¹⁷Hz to 7 x 10¹⁴Hz. It has less penetrating power. It can be absorbed by atmospheric ozone and harmful to human body. It is used to destroy bacteria, sterilizing the surgical instruments, burglar alarm, detect the invisible writing, finger prints and also in the study of molecular structure.

It provides electrical energy to satellites by means of solar cells. It is used to produce dehydrated fruits, in green houses to keep the plants warm, heat therapy for muscular pain or sprain, TV remote as a signal carrier, to look through haze fog or mist and used in night vision or infrared photography.

(i) If the electromagnetic wave incident on a material surface is completely absorbed, then the energy delivered is U, and momentum imparted on the surface is P = \(\frac{U}{c}\)
(ii) If the incident electromagnetic wave of energy U is totally reflected from the surface, then the momentum delivered to the surface is \(\Delta p=\frac { U }{ c } -\left( -\frac { U }{ c } \right) =2\frac { U }{ c } \)
(iii) The rate of flow of energy crossing a unit area is known as the pointing vector for electromagnetic waves.

i) Maxwell's prediction was experimentally confirmed by Heinrich Rudolf Hertz in 1888. The experimental set up used is shown in Figure.
ii) It consists of two metal electrodes which are made of small spherical metals. These are connected to larger spheres and the ends of them are connected to induction coil with very large number of turns. This is to produce very high electromotive force (emf).
iii) Since the coil is maintained at very high potential, air between the electrodes gets ionized and spark (spark means discharge of electricity) is produced.
iv) The gap between electrode (ring type - not completely closed and has a small gap in between) kept at a distance also gets spark. This implies that the energy is transmitted from electrode to the receiver (ring electrode) as a wave, known as electromagnetic waves.

v) If the receiver is rotated by 90° - then no spark is observed by the receiver. This confirms that electromagnetic waves are transverse waves as predicted by Maxwell.
vi) Hertz detected radio waves and also computed the speed of radio waves which is equal to the speed of light (3 x 10⁸m S^-1).