The Speed of EM Waves

Q. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170 second. The frequency of the wave is

1. 0.36 Hz
2. 1.47 Hz
3. 2.94 Hz
4. 0.73 Hz

Q. In an electromagnetic wave in free space, the root mean square value of the electric field is $E_{rms}=6V/m$. The peak value of the magnetic field is

1. $4.23\times {10}^{-8}T$
2. $1.41\times {10}^{-8}T$
3. $2.83\times {10}^{-8}T$
4. $0.70\times {10}^{-8}T$

Q. An $LC$ circuit contains inductance $L=1\mu \text{H}$ and capacitance $C=0.01\mu \text{F}$. The wavelength of electromagnetic wave generated is nearly

1. $0.5\text{m}$
2. $5\text{m}$
3. $190\text{m}$
4. $30\text{m}$

Q.

An electromagnetic wave travels in a medium with the speed of $2\times {10}^8\mathrm{m}/\mathrm{s}$. The relative permeability of the medium is $1$. Find the relative permittivity of the medium.

Q.

The oscillating magnetic field in a plane electromagnetic wave is given by: $B_y=\left(8\times {10}^{-6}\right)\sin \left[2\times {10}^{11}t+300\pi x\right]T$. Calculate the wavelength of the electromagnetic wave.

Q. When a ray of light of frequency $6\times {10}^{14}\text{Hz}$ travels from water of refractive index $\frac{4}{3}$ to glass of refractive index $\frac{8}{5}$, its

1. $\text{frequency becomes}\frac{5}{6}th\text{of its initial value}.$
2. $\text{speed becomes}\frac{5}{6}th\text{of its initial value}.$
3. $\text{wavelength becomes}\frac{6}{5}th\text{of its initial value}.$
4. $\text{speed becomes}\frac{6}{5}th\text{of its initial value}.$

Q.

How fast do electromagnetic waves travel in a vacuum?

Q.

A plane electromagnetic wave of frequency $500MHz$ is travelling in vacuum along $x,\hspace{0.17em}y,\hspace{0.17em}z$- direction. At a particular point in space and time, $\overrightarrow{B}=8.0\times {10}^{-8}\hat{z}T$ . The value of electric field at this point is: (speed of light$=3\times {10}^{8}m{s}^{–1}$) Assume $x,\hspace{0.17em}y,\hspace{0.17em}z$ are unit vectors along $\hat{x},\hat{y}\&\hat{z}$ directions.

1. $\begin{array}{l}2.6\hat{x}\frac{V}{m}\end{array}$

2. $\begin{array}{l}-2.6\hat{y}\frac{V}{m}\end{array}$

3. $\begin{array}{l}24\hat{x}\frac{V}{m}\end{array}$

4. $\begin{array}{l}-24\hat{x}\frac{V}{m}\end{array}$

Q.

How does the speed of electromagnetic wave in vacuum depend upon the source of radiation?

Q. In an apparatus, the electric field was found to oscillate with an amplitude of 18 V/m. The magnitude of the oscillating magnetic field will be

1. 4 X 10^-6 T
2. 6 X 10^-8 T
3. 9 X 10^-9 T
4. 11 X 10^-11 T

Q. An electric dipole of dipole moment p is placed along the x-axis. The angle made by electric field with x-axis at a point P, whose position vector makes an angle theta with x-axis, is: (where, tan alpha=(1/2) tan theta) (A) alpha (B) theta (C) theta + alpha (D) theta + 2*alpha

Q.

A string of length L fixed at both ends vibrates in its fundamental mode at a frequency v and a maximum apmplitude A. (a) Find the wavelength and the wave number k. (b) Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

Q.

If $c$ is the speed of electromagnetic waves in vacuum then $v$, its speed in a medium of dielectric constant $K$ and relative permeability ${\mu }_r$ is

1. $v=\frac{1}{\sqrt{{\mu }_{r}k}}$

2. $v=c\sqrt{{\mu }_{r}k}$

3. $v=\frac{c}{\sqrt{{\mu }_{r}k}}$

4. $v=k\sqrt{{\mu }_{r}c}$

Q. Light of wavelength $520\text{nm}$ passing through a double slit, produces interference pattern of relative intensity versus deflection angle $\theta$ as shown in the figure. Find the separation $d$ between the slits.

1. $1.98\times {10}^{-4}\text{m}$
2. $1.98\times {10}^{-5}\text{m}$
3. $1.98\times {10}^{-6}\text{m}$
4. $1.98\times {10}^{-7}\text{m}$

Q. Dimentional formula of permeability of free space ${\mu }_0$ is given by

1. $\left[M^{0}L{T}^{-2}{A}^{-2}\right]$
2. $\left[M{L}^2{T}^{-1}{A}^{-2}\right]$
3. $\left[ML{T}^{-2}{A}^{-2}\right]$
4. $\left[M^{0}L{T}^{-1}{A}^{-1}\right]$

Q. In a region of uniform electric field of magnitude $10\text{N/C}$, what will be the energy stored in a sphere of radius $3\text{m}?$

1. $5\times {10}^{-8}\text{J}$
2. $9\times {10}^{-8}\text{J}$
3. $4\times {10}^{-8}\text{J}$
4. $2\times {10}^{-8}\text{J}$

Q. A travelling wave represented by $y=A\sin (\omega t-kx)$ is superimposed on another wave represented by $y=A\sin (\omega t+kx)$. The resultant is

1. A standing wave having nodes at$x=(n+\frac{1}{2})\frac{\lambda }{2}$, where $n=0,1,2$
2. /a wavelength travelling along $-x$ direction
3. A wave travelling along $+x$ direction
4. a standing wave having nodes at $x=\frac{n\lambda }{2}$, where $n=0,1,2$

Q. Which of the given relations is correct {C is speed of light}

1. $C=\frac{1}{{\mu }_0{\epsilon }_0}$
2. $EB=C$
3. $E=BC$
4. $EC=B$

Q. Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye? [Take wavelength of light = 500 nm]

1. 6 m
2. 3 m
3. 5 m
4. 1 m

Q. Which of the given relations is correct?
$(c$ is speed of light, $E$ is electric field strength and $B$ is magnetic field strength$)$

1. $C=\frac{1}{{\mu }_0{\epsilon }_0}$
2. $EB=C$
3. $E=BC$
4. $EC=B$

Q. If the magnetic field in a plane electromagnetic wave is given by $\overrightarrow{B}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{j}\text{T}$ then what will be expression for electric field ?

1. $\overrightarrow{E}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{i}\text{V/m}$
2. $\overrightarrow{E}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{j}\text{V/m}$
3. $\overrightarrow{E}=60\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{k}\text{V/m}$
4. $\overrightarrow{E}=9\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{k}\text{V/m}$

Q. What are the directions of electric and magnetic field vectors relative to each other and relative to the direction of propagation of electromagnetic waves?

Q. An LC circuit contains an inductor and capacitor of $L=1\mu \text{H}\&C=0.01\mu \text{F}.$ The wavelength of electromagnetic wave generated is nearly

1. $0.5\text{m}$
2. $5\text{m}$
3. $190\text{m}$
4. $19\text{m}$
   

Q.

The frequency of incident light falling on a photosensitive metal plate is doubled, the kinetic energy of the emitted photoelectrons is

1. Unchanged
2. Less than doubled
3. Double the earlier value
4. More than doubled

Q. In T.V. broadcasting both picture and sound are transmitted simultaneously because :

1. both audio and video signals are frequency modulated
2. audio signal is frequency modulated and video signal is amplitude modulated
3. both audio and video signals are amplitude modulated
4. audio signal is amplitude modulated and video signal is frequency modulated

Q. The rms and the average value of the voltage wave shown in the figure are

1. $\sqrt{\frac{32}{3}}V;1V$
2. $\sqrt{\frac{11}{3}}V;1V$
3. $\sqrt{\frac{11}{3}}V;3V$
4. $\sqrt{\frac{32}{3}}V;3V$

Q. A radiation is emitted by $1000\text{W}$ bulb, and it generates electric field and magnetic field at $P$, placed at a distance of $2\text{m}$. The efficiency of the bulb is $1.25$%. The value of peak electric field at $P$ is $x\times {10}^{-1}\text{V/m}$. Value of $x$ is __________. $($Rounded-off to the nearest integer$)$
$[$Take ${ϵ}_o=8.85\times {10}^{-12}{\text{C}}^2{\text{/Nm}}^2,c=3\times {10}^8\text{m/s}]$

Q. Electrons with energy $80KeV$ are incident on the tungsten target of an X-ray tube. $K$ shell electrons of tungsten have $-72.5keV$ energy. X-rays emitted by the tube contain only :

1. A continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of $-0.155\mathring{A}$
2. A continuous X-ray spectrum (Bremsstrahlung) with all wavelengths
3. A continuous X-ray spectrum of tungsten
4. A continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of $-0.155\mathring{A}$ and the characteristic X-ray spectrum of tungsten

Q. A monochromatic light of wavelength 589 nm is incident from air onto water surface. The refractive index of water is 1.33. What is the wavelength and speed of refracted light?

1. $589nm,2.256\times {10}^{8}m{s}^{-1}$
2. $632nm,3\times {10}^{8}m{s}^{-1}$
3. $443nm,2.256\times {10}^{8}m{s}^{-1}$
4. $726nm,3\times {10}^{8}m{s}^{-1}$

Q. The speed of electromagnetic wave in vacuum depends upon the source of radiation. It

1. is same for all of them
2. decreases as we move from $\gamma$-rays to radio waves
3. increases as we move from $\gamma$-rays to radio waves
4. None of these