Wave Equation of EM Waves

Q.

The electric field ( in NC^-1) in an electromagnetic wave is given by $E=50\sin \omega (t-\frac{x}{c})$.The energy stored in a cylinder of cross-section $10c{m}^2$ and length $100cm$along the x-axis will be

1. $5.5\times {10}^{-12}J$

2. $1·1\times {10}^{-11}J$

3. $2·2\times {10}^{-11}J$

4. $1·65\times {10}^{-11}J$

Q. The electric field in an electromagnetic wave is given by $E=\left(50N{C}^{-1}\right)\sin \omega (t-\frac{x}{c})$.
Find the electrical energy contained in a cylinder of cross-section 10 $c{m}^2$ and length 50 $cm$ along the x-axis.

1. $5.5\times {10}^{-12}J$
2. $1.1\times {10}^{-8}J$
3. $5\times {10}^{-4}J$
4. $1.1\times {10}^{-12}J$

Q.

A sound wave of frequency $245Hz$ travels with a speed of $300m{s}^{-1}$ along the positive $x-axis$. Each point of the medium moves to and fro through a total distance of $6cm$. What will be the mathematical expression of the travelling wave?

1. $Y(x,t)=0.03[\sin 5.1x–(0.2\times {10}^3\left)t\right]$

2. $Y(x,t)=0.06[\sin 5.1x–(1.5\times {10}^3\left)t\right]$

3. $Y(x,t)=0.06[\sin 0.8x–(0.5\times {10}^3\left)t\right]$

4. $Y(x,t)=0.03[\sin 5.1x–(1.5\times {10}^3\left)t\right]$

Q. Twelve equal charges $\left(q\right)$, are situated at the corners of a regular $12-$sided polygon $($for instance, one on each numeral of a clock face$)$. What is the net force on a test charge $Q$ at the centre?
$($Assume the distance between $q$ and $Q$ pair(s) to be $L)$

1. $\frac{Qq}{4\pi {ϵ}_o{L}^2}$
2. $\frac{Qq}{2\pi {ϵ}_o{L}^2}$
3. $\frac{Qq}{3\pi {ϵ}_o{L}^2}$
4. Zero

Q.

The electric field of a plane electromagnetic wave varies with the time of amplitude $2V{m}^{-1}$propagating along the z-axis. The average energy density of the magnetic field is $(inJ{m}^{-3})$

1. $13.29\times {10}^{-12}$

2. $8.85\times {10}^{-12}$

3. $17.72\times {10}^{-12}$

4. $4.43\times {10}^{-12}$

5. $2.22\times {10}^{-12}$

Q.

What are some examples of electromagnetic waves?

Q.

The part of the electromagnetic spectrum which is suitable for radar systems used in aircraft navigation.

1. X - Rays

2. Gamma Rays

3. Microwaves or short radio waves

4. Ultraviolet

Q. A transmitting antenna has a height of $320\text{m}$ and that of receiving antenna is $2000\text{m}$. The maximum distance between them for satisfactory communication in line of sight mode is '$d$'. Then the value of '$d$' is $\text{km}$

Q. Force acting on charges separated by some distance is shown in the figure.


Select the correct relation between given parameters :

1. $q_1{q}_2>0,{\overrightarrow{F}}_{12}=-{\overrightarrow{F}}_{21}$
2. $q_1{q}_2<0,{\overrightarrow{F}}_{12}=-{\overrightarrow{F}}_{21}$
3. $q_1{q}_2>0,{\overrightarrow{F}}_{12}\ne {\overrightarrow{F}}_{21}$
4. $q_1{q}_2<0,{\overrightarrow{F}}_{12}=-2{\overrightarrow{F}}_{21}$

Q.

An AC source rated $220V,50Hz$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

1. $0.25ms$

2. $25ms$

3. $2.5ms$

4. $2.5s$

Q.

In an electromagnetic wave, the amplitude of electric field is 1 V/m. the frequency of wave is $5\times {10}^{14}$Hz. The wave is propagating along z-axis. The average energy density of electric field, in $Joule{m}^3$, will be

1. 1.1 X 10^-11
2. 3.3 X 10^-13
3. 2.2 X 10^-12
4. 4.4 X 10^-14

Q.

How do we use the electromagnetic spectrum in everyday life?

Q.

A plane electromagnetic wave is propagating along the direction$\begin{array}{l}\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\end{array}$with the polarization along the direction $\stackrel{\wedge }{k}$. The correct form of the magnetic field of the wave would be ( here $B_0$ is an appropriate constant)

1. $\begin{array}{l}{B}_0\left(\frac{\stackrel{\wedge }{i}-\stackrel{\wedge }{j}}{\sqrt{2}}\right)cos\left[\omega t-k\begin{array}{l}\left(\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\right)\end{array}\right]\end{array}$

2. $\begin{array}{l}{B}_0\left(\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\right)cos\left[\omega t+k\left(\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\right)\right]\end{array}$

3. $\begin{array}{l}{B}_0\left(\frac{\stackrel{\wedge }{i}-\stackrel{\wedge }{j}}{\sqrt{2}}\right)cos\left[\omega t+k\left(\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\right)\right]\end{array}$

4. $\begin{array}{l}{B}_0\stackrel{\wedge }{k}cos\left[\omega t-k\left(\frac{\stackrel{\wedge }{i}+\stackrel{\wedge }{j}}{\sqrt{2}}\right)\right]\end{array}$

Q.

A wave is propagating in a medium of electric dielectric constant 2 and relative magnetic permeability 50. The wave impedance of such a medium is

1. 5 Ω
2. 376.6 Ω
3. 1883 Ω
4. 3776 Ω

Q.

For an electromagnetic wave traveling in free space, the relation between average energy densities due to electric $\left(U_e\right)$and magnetic $\left(U_m\right)$ fields is :

1. $U_e\ne U_m$

2. $U_e=U_m$

3. $U_e>U_m$

4. $U_e<U_m$

Q.

In electromagnetic waves, the ratio of amplitudes of the electric field and the magnetic field is equal to

Q.

two charges are placed on the x-axis + 3 microcoulomb at X equal to zero and a charge of + 5 microcoulomb at X equal to 0.4 metre where must be a third charge placed if the force it experiences to be zero? Please show me how to calculate the answer with full steps

Test on Monday. Please explain faster

Q.

In the presence of an electric field, why does each electron experience a force -eE in the opposite direction?

Q.

A plane electromagnetic wave of frequency $100MHz$ is travelling in a vacuum along the x-direction. At a particular point in space and time,

$\begin{array}{l}\overrightarrow{B}=2.0\times {10}^{-8}kT\end{array}$ (where$\begin{array}{l}\hat{k}\end{array}$is the unit vector along the z-direction). What is $\begin{array}{l}\overrightarrow{E}\end{array}$ at this point? (speed of light, $c=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$)

1. $\begin{array}{l}0.6\hat{j}\frac{V}{m}\end{array}$

2. $\begin{array}{l}6.0\hat{k}\frac{V}{m}\end{array}$

3. $\begin{array}{l}6.0\hat{j}\frac{V}{m}\end{array}$

4. $\begin{array}{l}0.6\hat{k}\frac{V}{m}\end{array}$

Q. In order to establish an instantaneous displacement current of $1\text{mA}$ in the space between the plates of $2\mu F$ parallel plate capacitor, the potential difference need to apply is

1. $100{\text{Vs}}^{-1}$
2. $200{\text{Vs}}^{-1}$
3. $300{\text{Vs}}^{-1}$
4. $500{\text{Vs}}^{-1}$

Q.

Radiations of intensity $0.5W/m^2$ are striking a metal plate. The pressure on the plate is

1. $0.166\times {10}^{-8}N/m^2$

2. $0.332\times {10}^{-8}N/m^2$

3. $0.111\times {10}^{-8}N/m^2$

4. $0.083\times {10}^{-8}N/m^2$

Q.

Is Coulomb’s law universal law? Why?

Q.

TV waves have a wavelength range of 1-10 meter. Their frequency range in MHz is

1. 30-300

2. 3-30

3. 300-3000

4. 3-3000

Q. The intensity of gamma radiation from a given source is $I$ on passing through $36\text{mm}$ of lead it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be-

1. $6\text{mm}$
2. $9\text{mm}$
3. $18\text{mm}$
4. $12\text{mm}$

Q.

Which of the following statement is wrong

1. Infrared photon has more energy than the photon of visible light
2. Infrared rays are invisible but can cast shadows like visible light rays
3. Photographic plates are sensitive to ultraviolet rays
4. Photographic plates can be made sensitive to infrared rays

Q.

The magnetic field in a plane electromagnetic wave is given by
$B=\left(200\mu T\right)\sin \left[\right(4.0\times {10}^{15}{s}^{-1}\left)\right(t-\frac{x}{c}\left)\right]$
Find the maximum electric field and the average energy density corresponding to the electric field.

Q. To establish an instantaneous displacement current of magnitude $i\text{A}$ in between the plates of a parallel plate capacitor of capacitance $\frac{1}{2}\text{F}$, the value of $\frac{dV}{dt}$ is

1. $2i$
2. $\frac{i}{2}$
3. $\frac{1}{2i}$
4. $i$

Q. By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21%

1. 10%
2. 15%
3. 21%
4. 11%

Q.

what factors does electric field depend on?

Q.

Velocity of electromagnetic waves in a medium depends

1. only on the electrical properties of the medium

2. only on the magnetic properties of the medium

3. only on the mechanical properties of the medium

4. on none of these