Physics M.C.Q (1 Marks)

Velocity of light in a medium,
$\text{c}=\frac{1}{\sqrt{\mu_0\in_0\mu_\text{r}\in_\text{r}}}=\frac{1}{\mu_0\in_0}$

As we know, velocity of electromagnetic wave,
$\text{c}=\frac{1}{\sqrt{\mu_0\in_0}}=\frac{3\times10^8\text{m}}{\text{s}}$
which is constant
So It is independent of amplitude of electromagnetic wave, frequency and wavelength of electromagnetic wave.
so none of the above is correct.

Electromagnetic wave is a transverse wave that means the electric and magnetic field associated to it will not only be perpendicular to each other but will also be
perpendicular to the direction in which the wave travels.
So, if waves travel along $\hat{\text{k}}$ direction then the electric and the magnetic field will be along $\hat{\text{i}}$ and $\hat{\text{j}}$​ directions.

For a capacitor, we have:
$Q = CV$
If $Q$ is changing, there will be a current in capacitor plates,
$\text{I}=\frac{\text{dQ}}{\text{dt}}=\frac{\text{CdV}}{\text{dt}}$when voltage across the capacitor is constant, $\frac{\text{dV}}{\text{dt}}=0$
therefore,$ I = 0$
It implies that, for a $DC ($constant$)$ voltage, the capacitor current is zero.
Hence, for a $DC$ source the conduction current and displacement current $($capacitor current$)$ are not same.
Whereas, by Maxwell's equation for a time varying voltage $(AC$ voltage$),$ both conduction and displacement currents are same.

When frequency of microwave matches with frequency of water molecules i.e., resonant condition. Maximum energy is transferred to water molecules as their $K.E.$ energy.

Any stationary charge produce static electric field. And the field strength is given by:
$r$, is the radial distance from the point charge.
$Q,$ is the charge in Coulomb.
When electric charge oscillates electric field at any point also oscillates.And according to Maxwell's equations varying electric field produces magnetic field and an oscillating electric field produces oscillating magnetic field. This thing is used in antennas in which oscillating current of certain frequency produces oscillating electric and magnetic field which propagates through space $($electromagnetic waves$).$

Electromagnetic wave $V=3 \times 10^8 m / s$
Given frequency $(f) =10^9 Hz$
$\text{V}=\text{f}\lambda$
$\lambda=\frac{\text{V}}{\text{f}}$
$=\frac{3 \times 10^8} {10^9}$
$​= 0.3m$

An accelerated charge is the source of electromagnetic waves $\text{(EMWs)}$. When the charge is in a circular motion, the direction of its velocity continuously changes and thus it is in accelerated motion and produces $\text{EMWs}$. A charge falling in an electric field is accelerated by the electric force and thus produces $\text{EMWs.}$

Velocity of $EM$ wave $\text{v}=\frac{3\times10^8\text{m}}{\text{s}}$
Electric field vector $\text{E}=\frac{6\text{V}}{\text{m}}$
Thus magnetic field vector $\text{B}=\frac{\text{E}}{\text{v}}$
$\therefore\text{B}=\frac{6}{3\times10^8}=2\times10^{-8}\text{T}$

$v \rightarrow 2 vhv - hv v _0= KG _{\max }$
$So , KG _{\max }>2 KG _{\max }$
as $h v_0$ is constant

The speed of light, $\text{C}=\frac{1}{\sqrt{\mu_0\in_0}}$
The dimensions of $\frac{1}{\sqrt{\mu_0\in_0}}$ are of velocity, i.e., $\frac{\text{L}}{\text{T}}$
Therefore, $\frac{1}{\in_0\mu_0}$ will have dimensions $\frac{\text{L}^2}{\text{T}^2}$

According to Maxwell an accelerated charge produces a sinusoidal time varying magnetic field which in turn produces a time varying electric field .The two fields so produced are mutually perpendicular to each other and constitute an electromagnetic wave and propagate in space in the direction perpendicular to both the fields. An $AM$ wave is also an electromagnetic wave therefore its magnetic field component would be parallel to ground and perpendicular to the direction of propogation.

The matter$-$wave picture of electromagnetic wave/radiation elegantly incorporated the Heisenberg uncertainty principle.

Plane of polarization is a confinement of the electric/ magnetic field vector to a given plane along the direction of propagation. Therefore angle between them is $0^\circ .$

Radio Waves are generally in the frequency range $➔ 500\ kHz$ to $1000\ MHz$. Radio waves are used for long$-$distance communication, such as in television, mobiles, and radios. These devices receive radio waves and convert them to mechanical vibrations in the speaker to create sound waves.

The phase difference between electric and magnetic fields in an electromagnetic wave is$\pi$.

$X-$Rays are used to investigate the structure of solids.

The same amount of energy passes through equal areas parallel to the $yz$ plane as the wave travels in the $+x$ direction, so the amplitude and the intensity, which is proportional to the square of the amplitude, do not change.

Maxwell added the concept of displacement current in AMpere Circuit Law which governs the conduction in the wire of conduction current. After the deviation compass between capacitor Maxwell thought of magnetic lines which would be the result of varying current known as displacement current. So by continuing the displacement in Amperes law, Maxwell was able to show the result of Amperes conduction in circuit moving electrons and also the result of faraday generation of $ME$ waves.

Displacement current inside a capacitor is given by:-
$\text{i}_\text{d}=\in_0\frac{\phi\text{E}}{\text{dt}}$
where $\phi_\text{E}$​ is the electric flux inside the capacitor
The displacement current is developed inside a capacitor when there is a change in the electric flux linked with the capacitor.
The change in electric flux can occur in both the cases either the charge increases or decreases on the capacitor. This will lead to a change in flux linked with the coil.

The plane of polarisations is that plane in which there is no vibration. While a plane including the direction of light propagation and the direction of electric field is called the plane of vibration. The angle between them is $90^\circ .$

According to Ampere$-$Maxwell's Law, a magnetic field is produced due to the conduction current in a conductor and the displacement current. The conduction current is actually the motion of the charge. The displacement current is due to the changing electric field. The displacement current is given by,
$\text{i}_\text{d}=\in_0\frac{\text{d}\phi_\text{E}}{\text{dt}}$ $\big(\because\phi_\text{E}$ is the electric flux$\big)$
Thus, the magnetic field is produced by the moving charge as well as the electric field.

Key concept: When a wave is reflected from a denser medium or perfectly reflecting wall made with optically inactive material, then the type of wave doesn't change but only its phase changes by $180^\circ $ or $\hat{\text{I}}€$ radian.

The electric field is always perpendicular to the magnetic field, and both fields are directed at right$-$angles to the direction of propagation of the wave. In fact, the wave propagates in the direction $\overrightarrow{\text{E}}\times\overrightarrow{\text{B}}$ Electromagnetic waves are clearly a type of transverse wave.

The energy of electromagnetic waves is directly proportional to the frequency of the electromagnetic waves. So the order of frequency is given as:
$v_{\text {micro }} < v_{\text {infrared }}$ Since $E=h v$
$\rightarrow E \propto v$
The order of energy is as follows:
$E _{\text {micro }} < E _{\text {infrared }} < E _{\text {visible }} < E _{\text {ultraviolet }} < E _{\text {gamma }}$

Intensity or power per unit area of the radiations,
$P = pv$
$\Rightarrow\text{P}=\frac{\text{P}}{\text{v}}=\frac{0.5}{3\times10^8}=\frac{0.166\times10^{-8}\text{N}}{\text{m}^2}$

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying.
Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.
Here, the current in the outer circuit is $0.15 A$. Thus $0.15A$ will be the displacement current.