# Wave Equation of EM Waves

## Trending Questions

**Q.**

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

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

$1\xb71\times {10}^{-11}J$

$2\xb72\times {10}^{-11}J$

$1\xb765\times {10}^{-11}J$

**Q.**The electric field in an electromagnetic wave is given by E=(50 NC−1)sin ω(t−xc).

Find the electrical energy contained in a cylinder of cross-section 10 cm2 and length 50 cm along the x-axis.

- 5.5×10−12J
- 1.1×10−8J
- 5×10−4J
- 1.1×10−12J

**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?

$Y(x,t)=0.03[\mathrm{sin}5.1x\u2013(0.2\times {10}^{3}\left)t\right]$

$Y(x,t)=0.06[\mathrm{sin}5.1x\u2013(1.5\times {10}^{3}\left)t\right]$

$Y(x,t)=0.06[\mathrm{sin}0.8x\u2013(0.5\times {10}^{3}\left)t\right]$

$Y(x,t)=0.03[\mathrm{sin}5.1x\u2013(1.5\times {10}^{3}\left)t\right]$

**Q.**Twelve equal charges (q), 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)

- Qq4πϵoL2
- Qq2πϵoL2
- Qq3πϵoL2
- 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 $(inJ{m}^{-3})$

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

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

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

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

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

**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.

X - Rays

Gamma Rays

Microwaves or short radio waves

Ultraviolet

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

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

Select the correct relation between given parameters :

- q1q2>0, →F12=−→F21
- q1q2<0, →F12=−→F21
- q1q2>0, →F12≠→F21
- q1q2<0, →F12=−2→F21

**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:

$0.25ms$

$25ms$

$2.5ms$

$2.5s$

**Q.**

In an electromagnetic wave, the amplitude of electric field is 1 V/m. the frequency of wave is 5× 1014Hz. The wave is propagating along z-axis. The average energy density of electric field, in Joulem3, will be

- 1.1 X 10
^{-11} - 3.3 X 10
^{-13} - 2.2 X 10
^{-12} - 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)

$\begin{array}{l}{B}_{0}\left(\frac{\stackrel{\wedge}{i}-\stackrel{\wedge}{j}}{\sqrt{2}}\right)cos\left[\omega t-k\begin{array}{l}\left(\frac{\stackrel{\wedge}{i}+\stackrel{\wedge}{j}}{\sqrt{2}}\right)\end{array}\right]\end{array}$

$\begin{array}{l}{B}_{0}\left(\frac{\stackrel{\wedge}{i}+\stackrel{\wedge}{j}}{\sqrt{2}}\right)cos\left[\omega t+k\left(\frac{\stackrel{\wedge}{i}+\stackrel{\wedge}{j}}{\sqrt{2}}\right)\right]\end{array}$

$\begin{array}{l}{B}_{0}\left(\frac{\stackrel{\wedge}{i}-\stackrel{\wedge}{j}}{\sqrt{2}}\right)cos\left[\omega t+k\left(\frac{\stackrel{\wedge}{i}+\stackrel{\wedge}{j}}{\sqrt{2}}\right)\right]\end{array}$

$\begin{array}{l}{B}_{0}\stackrel{\wedge}{k}cos\left[\omega t-k\left(\frac{\stackrel{\wedge}{i}+\stackrel{\wedge}{j}}{\sqrt{2}}\right)\right]\end{array}$

**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

- 5 Ω
- 376.6 Ω
- 1883 Ω
- 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 :

${U}_{e}\ne {U}_{m}$

${U}_{e}={U}_{m}$

${U}_{e}>{U}_{m}$

${U}_{e}<{U}_{m}$

**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$}\right.$)

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

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

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

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

**Q.**In order to establish an instantaneous displacement current of 1 mA in the space between the plates of 2 μF parallel plate capacitor, the potential difference need to apply is

- 100 Vs−1
- 200 Vs−1
- 300 Vs−1
- 500 Vs−1

**Q.**

Radiations of intensity 0.5W/m2 are striking a metal plate. The pressure on the plate is

0.166× 10−8 N/m2

0.332× 10−8 N/m2

0.111× 10−8 N/m2

0.083× 10−8 N/m2

**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

30-300

3-30

300-3000

3-3000

**Q.**The intensity of gamma radiation from a given source is I on passing through 36 mm of lead it is reduced to I8. The thickness of lead which will reduce the intensity to I2 will be-

- 6 mm
- 9 mm
- 18 mm
- 12 mm

**Q.**

Which of the following statement is wrong

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

**Q.**

The magnetic field in a plane electromagnetic wave is given by

B=(200μT)sin[(4.0×1015s−1)(t−xc)]

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 A in between the plates of a parallel plate capacitor of capacitance 12 F, the value of dVdt is

- 2i
- i2
- 12i
- 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%

- 10%
- 15%
- 21%
- 11%

**Q.**

what factors does electric field depend on?

**Q.**

Velocity of electromagnetic waves in a medium depends

only on the electrical properties of the medium

only on the magnetic properties of the medium

only on the mechanical properties of the medium

on none of these