Tag: physics

Questions Related to physics

An electromagnetic wave is propagating along x-axis. At x = 1 m and t = 10 s, its electric vector |$\overset{-}{E}|  = 6 V/m$ then the magnitude of its magnetic vector is:

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $2 \, \times \, 10^{-8} \, T$

  2. $3 \, \times \, 10^{-7} \, T$

  3. $6 \, \times \, 10^{-8} \, T$

  4. $5 \, \times \, 10^{-7} \, T$

Show answer
Correct Option: A
Explanation:

Electric and magnetic compounds of an electromagnetic field are related by 

$E = CB$
$B = \dfrac{E}{C}$
$B = \dfrac{6}{3 \times 10^8}$  (when $E$ is given)
$B = 2 \times 10^{-8} T$ 

The electric field associated with an electromagnetic wave in vacuum is given by $|\overrightarrow { E } |= 40\ cos (kz -6\times{10}^{8}t )$, where $E$, $z$ and $t$ are in volt per meter, meter and second respectively. The value of wave vector $k$ is:

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $2\ {m}^{-1}$

  2. $0.5\ {m}^{-1}$

  3. $3\ {m}^{-1}$

  4. $6\ {m}^{-1}$

Show answer
Correct Option: A
Explanation:

Given: The electric field associated with  an electromagnetic wave in vacuum is given by $|\vec E|=40 \cos(kz−6\times 10^8t)$


To find: Value of wave vector $k$


Solution: 
We know electromagnetic wave eqution is
$|\vec E|=E _0\cos(kz-\omega t)$

And given equation is
$|\vec E|=40 \cos(kz−6\times 10^8t)$

By comparing these two, we get
$\omega=6\times10^8$ and 
$E _0=40$

We also know,
Speed of electromagnetic wave is given by:
$v=\dfrac \omega k$
where v is the speed of the light.

Hence, 
$k=\dfrac \omega v\\\implies k=\dfrac {6\times 10^8}{3\times 10^8}\\\implies k=2m^{-1}$

Option $(A)$ is correct.

The velocity of electromagnetic waves in a dielectric medium $\left( { \varepsilon  } _{ r }=2 \right) $ is:

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $3\times { 10 }^{ 8 }$ meter/second

  2. $1.5\times { 10 }^{ 8 }$ meter/second

  3. $6\times { 10 }^{ 8 }$ meter/second

  4. $7.5\times { 10 }^{ 7 }$ meter/second

Show answer
Correct Option: B
Explanation:
It turns out that electromagnetic waves cannot propagate very far through a conducting medium before they are either absorbed or reflected. However, electromagnetic waves are able to propagate through transparent dielectric media without difficultly. The speed of electromagnetic waves propagating through a dielectric medium is given by 
$c'=\dfrac{c}{\epsilon _r}$

If the relative permeability of a medium is $ \mu _r$ and its dielectric constant is  $\varepsilon _r$ then the velocity of light in that medium will be

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $ \sqrt{\dfrac { \mu _r }{ { { \varepsilon } _{ r } } }} $

  2. $ \dfrac { 1 }{ \sqrt { { \mu } _{ r }{ \varepsilon } _{ r } } } $

  3. $ \sqrt { { \mu } _{ r }{ \varepsilon } _{ r }/{ \mu } _{ { \varepsilon } _{ 0 } } } $

  4. $ \sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 }/{ \mu } _{ { r } }{ \varepsilon } _{ r } } $

Show answer
Correct Option: B
Explanation:

$c=\dfrac{1}{\sqrt{\epsilon _0\mu _0}}$

$v=\dfrac{1}{\sqrt{\epsilon\mu}}=\dfrac{1}{\sqrt{\epsilon _0\epsilon _r\mu _0\mu _r}}$
$=\dfrac{c}{\sqrt{\epsilon _r\mu _r}}$

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

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. increases as we move from $\gamma$-rays to radio waves

  2. decreases as we move from $\gamma$-rays to radio waves

  3. is same for all of them

  4. None of these

Show answer
Correct Option: C
Explanation:

$Answer:-$ C

speed of electromagnetic wave in vacuum  is given by:-
c(speed of light)=frequency$\times$ wavelength =$\dfrac{1}{\mu _0 \epsilon _0}$=constant
as we go from gamma rays to radio waves  frequency decreases and wavelength increases thereby maintaining the product constant.

The electromagnetic waves travel with a velocity

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. equal to velocity of sound.

  2. equal to velocity of light.

  3. less than velocity of light.

  4. None of the above.

Show answer
Correct Option: B
Explanation:

Velocity of electromagnetic waves $\displaystyle=\dfrac{1}{\mu _0\epsilon _0}=3\times{10}^8:m/s=$ velocity of light.

The speed of electromagnetic wave is same for

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. odd frequencies

  2. even frequencies

  3. all frequencies

  4. all intensities

Show answer
Correct Option: D
Explanation:

The speed of electromagnetic wave in a region is same for all intensities but different for different frequencies.

The formula for the velocity of electromagnetic waves in vacuum is given by

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $c = \sqrt{\mu _0 \varepsilon}$

  2. $c = \dfrac{1}{\sqrt{\mu _0 \varepsilon _0}}$

  3. $c = \sqrt{\dfrac{\mu _0}{\varepsilon _0}}$

  4. $c = \sqrt{\dfrac{\varepsilon _0}{\mu _0}}$

Show answer
Correct Option: B
Explanation:

Maxwell deduced that the speed of propagation of an electromagnetic wave through a vacuum is entirely determined by the constants $\mu _0$ and $\epsilon _0$ as the following:
$c=\frac{1}{\sqrt{\mu _0 \epsilon _0}}$
We know that   $\mu _0 = 4\pi\times 10^{-7}\,{\rm N}\,{\rm s}^2 \,{\rm C}^{-2}$ and  $\epsilon _0 = 8.854\times 10^{-12}\,{\rm C}^2\,{\rm N}^{-1} \,{\rm m}^{-2}$ which gives:
$c=\frac{1}{\sqrt{4 \pi \times 10^{-7} 8.854 \times 10^{-12}}} = 2.998 \times 10^8$ m/s

The amplitudes $E _{0}$ and $B _{0}$ of electric and the magnetic component of an electromagnetic wave respectively are related to the velocity $c$ in vacuum as

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $E _{0}B _{0} = \dfrac {1}{c}$

  2. $E _{0} = \dfrac {c}{B _{0}}$

  3. $B _{0} = cE _{0}$

  4. $E _{0} = cB _{0}$

  5. $E _{0} = c^{3}B _{0}$

Show answer
Correct Option: D
Explanation:

As we know, in electromagnetic waves, speed or light,
$c = \dfrac {E _{0}}{B _{0}} \Rightarrow E _{0} = cB _{0}$.

An electromagnetic wave passing through the space is given by equations $E=E _o\sin(wt-kx), B=B _0\sin(wt-kx)$ which of the following is true?

physics option a: relativity the nature of light speed of light and optical density introduction to light

  1. $E _oB _0=wk$

  2. $E _ow=B _ok$

  3. $E _ok=B _ow$

  4. $E _owk=B _o$

Show answer
Correct Option: C
Explanation:

As $\dfrac{E _o}{B _o}=c$ (a)

where $c=$speed of light
$c=\nu \lambda$
Also
$w=2\pi \nu$ (1)
$k=\dfrac{2\pi}{\lambda}$ (2)
Dividing (2) by (1)
$\dfrac{w}{k}=\dfrac{2\pi \nu}{\dfrac{2\pi}{\lambda}}=\nu \lambda=c$ 
Hence (a) becomes
$\dfrac{E _o}{B _o}=\dfrac{w}{k}$
$E _ok=B _ow$
Hence the correct option is (C).