Physics M.C.Q (1 Marks)

For an electromagnetic wave,electric field, magnetic field and direction of propagation are mutually perpendicular to each other. We can have a region in which electric and magnetic fields are applied at an angle with each other. In transmission lines Different modes exist. In transverse electric $(TE)$ mode$-$no electric field exist in the direction of propagation. These are sometimes called $H$ modes because there is only a magnetic field along the direction of propagation $($His the conventional symbol for magnetic field$).$

Electromagnet waves have electric field as well as magnetic field which are perpendicular to each other and the electromagnetic waves propagate in a direction
which is perpendicular to both the fields.
Thus the propagation vector of $EM$ waves $\overrightarrow{\text{k}}=\overrightarrow{\text{E}}\times\overrightarrow{\text{B}}$

Axis of propagation always lie perpendicular to the plane of vibrations, therefor angle between them is $\frac{\pi}{2}$

The compass needle deflects due to the presence of the magnetic field. Inside the capacitor, a magnetic field is produced when there is a changing electric field inside it. As the capacitor is connected across the battery, the charge on its plates at a certain time tis given by,
$\text{Q}=\text{CV}\Big(1-\text{e}^{-\tau/\text{RC}}\Big),$
$Q =$ Charge developed on the plates of the capacitor.
$R =$ Resistance of the resistor connected in series with the capacitor.
$C =$ Capacitance of the capacitor.
$V =$ Potential difference of the battery.
The time constant of the capacitor is given, $\tau=\text{RC}$
The capacitor keeps on charging up to the time $\tau$. The development of charge on the plates will be gradual after $​​\tau=\text{RC}$ The change in electric field will be up to the time the charge is developing on the plates of the capacitor. Thus, the compass needle deflects and gradually comes to the original position in a time that is large compared to the time constant.

Key concept: A changing electric field produces a changing magnetic field and vice versa which gives rise to a transverse wave known as electromagnetic wave. The time varying electric and magnetic field are mutually perpendicular to each other and also perpendicular to the direction of propagation of this wave. The electric vector is responsible for the optical effects of an $EM$ wave and is called the light vector.


The direction of propagation of electromagnetic wave is perpendicular to both electric field vector $(\vec{\text{E}})$ and $\vec{\text{B}}$ magnetic field vector $B$, i.e., in the direction of $\vec{\text{E}}\times\vec{\text{B}}$.
Here, elecromagnetic wave is along the $z-$direction which is given by the cross product of $E$ and $B.$

Time period, $\text{T}=\frac{1}{\text{v}}$
$\text{T}=\frac{1}{40\times10^6}$
$\Rightarrow\text{T}=0.25\mu\text{s}$

Human eye is sensitive to light of wavelength $\rightarrow \lambda=5550$ angstrom.
So its frequency is $v =\frac{ c }{\lambda}$
$v=\frac{5550}{3 \times 10^8} \times 10^{-10}$
$v=5.405 \times 10^{14} Hz$

All the longitudinal waves like sound etc cannot be polarized because the motion of the particles is already in one dimension that is the direction of propagation of wave.
Thus all the transverse waves like electromagnetic waves can be polarized.
Thus, $(B)$ Ultrasonic waves being sound waves having frequency greater than $20\ kHz$ but being longitudinal in nature cannot be polarized

Light waves and $X-$rays are electromagnetic waves.

$e = E \times B$, direction of propagation is always perpendicular to plane of $E$ and $B$. It will be positive in x-direction.

Radiation pressure is given by $\text{P}_\text{R}=\frac{(1+\alpha)\text{I}}{\text{C}}$
where α is the coefficient of reflection of the surface.
For completely reflecting surface $\alpha=1$
For completely absorbing surface $\alpha=0$
So, radiation pressure depends on the nature of surface on which the light is falling but independent of wavelength of light falling.

Microwaves have wavelength around $10\ cm.$

The wave equation for a plane electric wave traveling in the $x$ direction in space is
$\frac{\delta^2\text{E}}{\delta^2\text{y}}=\frac{1}{\text{c}^2}\frac{\delta^2\text{E}}{\delta\text{t}^2}$
with the same form applying to the magnetic field wave in a plane perpendicular the electric field. Both the electric field and the magnetic field are perpendicular to the direction of travel $y.$

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 $\text{EMWs.}$

For any given medium, the speed $(c)$ of an electromagnetic wave is given by,
$\text{C}=\text{v}\lambda$
Where,
$V =$ Frequency of the electromagnetic wave.
$\lambda=$ wavelength of the electromagnetic wave.
As the frequency and wavelength are changed, the speed of the electromagnetic wave changes. So, the speed of an electromagnetic wave is not same for all wavelengths and all frequencies in any medium. The velocity of an electromagnetic wave changes with change in medium. Also, the speed of an electromagnetic wave is same for all the intensities in any medium.

The ratio of frequencies of $UV$ rays and $IR$ rays in the glass is more than $1$. This is because the frequency of $UV$ rays is greater than that of infrared rays. This situation is applicable in glass or vacuum or air.

As we know, $\text{E}\propto\text{R}^{-2}$
Therefore, $\text{E}(\text{R}=5)=\frac{500}{10^{-2}}5^{-2}=\frac{2000\text{V}}{\text{m}}$

For electromagnetic waves $E$ and $B$ are always perpendicular to each other and perpendicular to the direction of propagation. The direction of propagation is the direction of $E \times B.$
The direction of propagation of the wave is the direction of propagation of its energy and power.

A diode antenna radiates the electromagnetic waves outwards. The amplitude of electric field vector $\left(E_0\right)$ which transports significant energy from the source falls intensity inversely as the distance $(r)$ from the antenna, i.e., $E _0 \propto \frac{1}{ r }$.

In a capacitor of capacitance $C,$
$\text{V}=\frac{\text{q}}{\text{C}}$
$\Rightarrow\frac{\text{dV}}{\text{dt}}=\frac{\text{i}}{\text{C}}=\frac{1\text{A}}{1\mu\text{F}}=\frac{10^6\text{V}}{\text{s}}$

The general equation of an electromagnetic wave is $B = A \sin ( kx +\omega t )$
Comparing this equation with the given equation, $A =2 \times 10^{-7}, k =10^3$ and $\omega=1.5 \times 10^{12}$
So, $10^3=\frac{2 \pi}{\lambda}$
or $\lambda=6.28 \times 10^{-3} m=6.28 mm$

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.

$\text{B}=\frac{\text{E}}{\text{C}}$
$=\frac{9.3}{3\times10^8}$
$=3.1\times10^{-8}$

$\text{k}=\frac{2\pi}{\lambda}$
$\omega=\frac{2\pi\text{c}}{\lambda},$ where c is the velocity of light
Hence, $=\frac{\text{k}}{2\pi}=\frac{\omega}{2\pi\text{c}}$
$\Rightarrow\frac{\text{k}}{\omega}$ is independent of the wavelength.