Tag: the nature of light

Questions Related to the nature of light

The electric field associated with an e.m. wave in vacuum is given by $\vec {E} = 40\cos (kz - 6\times 10^{8}t)\hat {i}$, where $E, z$ and $t$ in $volt/m$, meter and seconds respectively. The value of wave vector $k$ is

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. $6m^{-1}$

  2. $3m^{-1}$

  3. $2m^{-1}$

  4. $0.5m^{-1}$

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Correct Option: C
Explanation:
Given: The electric field associated with  an electromagnetic wave in vacuum is given by $\vec E =40 \cos(kz−6\times 10^8t)\hat i$  , where E, z and t are in volt per meter, meter and second respectively.
To find the value of wave vector k
Solution: 
We know electromagnetic wave eqution is
$E=E _0\cos(kz-\omega t)$
And given equation is
$\vec E =40 \cos(kz−6\times 10^8t)\hat i$
By comparing these two, we get
$\omega=6\times10^8$ and 
$E _0=40\hat i$
we also know,
Speed of electromagnetic wave, $v=\dfrac \omega k$
where v is the speed of the light
Hence, $k=\dfrac \omega v\\\implies k=\dfrac {6\times 10^8}{3\times 10^8}\\\implies k=2m^{-1}$
is the required value

Wavelength of light in different media are proportional to:

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. speed of light in that medium

  2. Amplitude of light in that medium

  3. frequency of light in that mrdium

  4. Nove of above

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Correct Option: A

The Maxwell's equation : $\oint \vec { \mathrm { B } }$ . $\vec { \mathrm { d } 1 } = \mu _ { 0 } \left( \mathrm { i } + \varepsilon _ { 0 } \cdot \frac { \mathrm { d } \phi _ { \mathrm { E } } } { \mathrm { dt } } \right)$ is a statement of

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. Faraday's law of induction

  2. Modified Ampere's law

  3. Gauss's law of electricity

  4. Gauss's law of magnetism

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Correct Option: A

What is the displacement current between the square plate of side 1 cm of a capacitor, if electric field between the, plates is changing at the rate of 3 x $10^6 V _m^{-1}S^{-1}$? 

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. 2.7 x $10^{-6}$ A

  2. 3.2 x $10^{-6}$ A

  3. 4.2 x $10^{-6}$ A

  4. 4.0 x $10^{-6}$ A

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Correct Option: B

In Maxwell's velocity distribution curve area under the graph 

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. Increases when temperature is increased

  2. Deccreases when temperature is increased

  3. Remains same at all temperature

  4. Depends on the pressure of the gas

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Correct Option: C
Explanation:

Area under the Maxwell's velocity distribution curve gives the number of particles. Since number of particles remains the same at all the temperatures, so the area under the curve also remains the same at all temperature.

If a plane electromagnetic wave satisfies the equation $\dfrac{\partial ^2E _x}{\partial _z^2}= C^2 \dfrac{\partial^2E _x}{\partial^2},$the wave propagates in

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. $x$-direction

  2. $z$-direction

  3. $y$-direction

  4. $xz$ plane at an angle of $45^0$ between the $x$ and $z$direction

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Correct Option: A

According to the electromagnetic wave theory, light consists of electric and magnetic fields which are __________.

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. parallel to each other

  2. perpendicular to each other

  3. inclined at an angle of ${45}^{o}$ to each other

  4. none of these

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Correct Option: B
Explanation:

Light consists of electric and magnetic field that are perpendicular ${ 90 }^{ 0 }$ to each other.
APPOACH by example
Electric field inside plates. The magnetic field this given rise to via the displacement current is along the perimeter of the circle parallel to capauatates plates.

So B and E are perpendicular in this case.

Which of the following conclusion can be drawn from the result $\oint \bar{B}\cdot d\bar{A}=0$

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. Magnetic field is zero everywhere

  2. Magnetic monopole cannot exist

  3. Magnetic lines of force do not intersect each other

  4. A current produces magnetic field

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Correct Option: B
Explanation:

Flux of certain closed surface is zero and so it tells that net magnetic charge is equal to zero. This is possible when there are two equal and opposite poles.

Which of the following effects could not be explained by Maxwell's electromagnetic wave theory?

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. Photoelectric effect

  2. Compton effect

  3. Raman effect

  4. All of these

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Correct Option: D
Explanation:

  1. Photoelectric effect was discovered by heinrich Rudoy Hertz.
  2. Compton effect was discovered by Aethur Holl Compton.
  3. Raman effect was discovered by Sir Chandrasekhar Venbata Ram. 
      So, none of these effect was discovered by Maxwell.

A parallel plate capacitor having plate area A and plate separation $d$ is connected to a battery of emf $\varepsilon$ and internal resistance $R$ at $t=0$. Consider a plane surface of area $\dfrac{A}{2}$, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time?

physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

  1. $\dfrac {-\varepsilon}{2R} \ \ \ e^{\dfrac{-td}{\varepsilon AR}}$

  2. $\dfrac {2\varepsilon}{R} \ \ \ e^{\dfrac{-td}{\varepsilon AR}}$

  3. $\dfrac {5\varepsilon}{2R} \ \ \ e^{\dfrac{-td}{4 \varepsilon AR}}$

  4. $\dfrac {\varepsilon}{2R} \ \ \ e^{\dfrac{-td}{4\pi \varepsilon AR}}$

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Correct Option: A