Tag: the nature of light

Questions Related to the nature of light

Choose the correct answer from the alternatives given.
A plane electromagnetic wave of frequency $25 MHz$ travels in free space along $X$-direction. At a particular point in space and time, electric field $\vec E=6.3\ \hat j\ V/m$. What is $B$ at this point.

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

  1. $1.2 \, \times \, 10^{-6} \, T$

  2. $1.2 \, \times \, 10^{-8} \, T$

  3. $2.1 \, \times \, 10^{-6} \, T$

  4. $2.1 \, \times \, 10^{-8} \, T$

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Correct Option: D
Explanation:

Given: The frequency of the electromagnetic wave is $25\ MHz$.

The electric field at the particular point is $6.3\hat j\ V/m$

To find: The magnetic field at that point.

The magnetic field of the electromagnetic wave at a point is given by:
$B = \dfrac{E}{c}\= \dfrac{6.3}{3 \times 10^8}\ \Rightarrow2.1 \times 10^{-8} T$

So, option $(D)$ is correct.

The electric field of an electromagnetic wave traveling through the vacuum is given by the equation $E=E _0\ sin (Kx-\omega t).$ The quantity that is independent of wavelength is:

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

  1. $k\omega$

  2. $\dfrac{k}{\omega}$

  3. $k^2\omega$

  4. $\omega$

Show answer
Correct Option: B
Explanation:

To find: The quantity that is independent of the wavelength.


The angular frequency $\omega$ is given by:
$\omega \, = \, 2\pi \nu$
The frequency of a wave varies with the wavelength. So, angular frequency is dependent on wavelength.

The quantity $k$ is defined as the wavenumber and it is given by:
$k = \dfrac{2\pi}{\lambda}$
It shows that $k$ is dependent on wavelength.


The value of $\dfrac{k}{\omega}$ can be obtained as:
$\dfrac {k}{\omega} \, = \, \dfrac{2\pi / \lambda}{2\pi \nu}\\implies \, \dfrac{1}{\nu \lambda} \, = \, \dfrac{1}{c}\,\,\ \ \ \ \ \ \ \ \ \ \ \ \  (\because \, c \, = \, \nu \lambda)$
where c is the speed of electromagnetic wave in vacuum. It is a constant whose value is $3 \, \times \, 10^8 \, ms^{-1}$.

So, option $(B)$ is correct.

Maxwell in his famous equations of electromagnetism, introduced the concept of

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

  1. ac current

  2. displacement current

  3. impedance

  4. reactance

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Correct Option: B
Explanation:

Maxwell's equations are:

1. $\nabla .E=\rho / \epsilon$
2. $\nabla.B=0$
3. $\nabla \times E= -\dfrac{dB}{dt}$
4. $\nabla \times B= \mu _0J+ \dfrac{1}{c^2} \dfrac{dE}{dt}$
so, considering the last eqn. written,
$\nabla \times B=\mu _0 J$ is the Ampere's eqn.
so, Maxwell modified the Ampere's eqn. and introduced the concept of displacement current.
So, displacement current =$\dfrac{1}{c^2} \dfrac{dE}{dt}$

Hence the correct option is $(B)$

$X-$ray falling on a material 

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

  1. Exerts a force on it

  2. Transfer energy to it

  3. Transfers momentum to it

  4. Transfers impules to it

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Correct Option: B
Explanation:

The emitted X-rays transfer energy to the material on which it is falling.

A parallel plate capacitor of plate separation 2 mm is connected in an electric circuit having source voltage 400. What is the value of the displacement current for $10^{-6}$ s, if plate area is 60 $cm^2$

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

  1. $1.062 \times 10^{-2} \ A$

  2. $2.062 \times 10^{-2} \ A$

  3. $3.062 \times 10^{-2} \ A$

  4. $5.062 \times 10^{-2} \ A$

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Correct Option: B

The displacement current flows in the dielectric of a capacitor when the potential difference across its plates

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

  1. becomes zero

  2. has assumed a constant value

  3. is increasing with time

  4. is decreasing with time

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Correct Option: C
Explanation:

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying. Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.  When a D.C voltage applied across its plates, constant voltage appears across its plates and so there will be no displacement current flowing through the capacitor. Thus the displacement current will flow when the potential is increasing with time.

The displacement current was first populated by

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

  1. Maxwell

  2. Marconi

  3. Ampere

  4. Hertz

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Correct Option: A
Explanation:

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field.

According to Maxwell's equation, the velocity of light in any medium is expressed as

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

  1. $\displaystyle\frac{1}{\sqrt{\mu _0\varepsilon _o}}$

  2. $\displaystyle\frac{1}{\sqrt{\mu\varepsilon}}$

  3. $\displaystyle\sqrt{\frac{\mu}{\varepsilon}}$

  4. $\displaystyle\sqrt{\frac{\mu _0}{\varepsilon}}$

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Correct Option: B
Explanation:

Velocity of light in a medium,

$\displaystyle c=\frac{1}{\sqrt{\mu _0\varepsilon _o\mu _r\varepsilon _r}}=\frac{1}{\sqrt{\mu\varepsilon}}$

Maxwell's equation describe the fundamental laws of

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

  1. electricity

  2. magnetism

  3. mechanics

  4. both (A) and (B)

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Correct Option: D
Explanation:

Maxwell's equation describe the fundamental laws of electricity and magnetism. His equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

According to Maxwell's hypothesis, a changing electric field gives rise to

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

  1. an electromagnetic force

  2. electric displacement current

  3. magnetic field

  4. pressure gradient

Show answer
Correct Option: C
Explanation:
$Answer:-$ C option
$\nabla \times B={ \mu  } _{ 0 }(J+{ \epsilon  } _{ 0 }\dfrac { dE }{ dt } )$
using this equation of maxwell we can say changing electric field $\dfrac{dE}{dt}$ induces magnetic field.