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Maxwell's equations - class-XI

Description: maxwell's equations
Number of Questions: 23
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Tags: electromagnetic waves and communication system electromagnetic waves physics option a: relativity
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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. $2.1 \, \times \, 10^{-8} \, T$

Show answer
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

Show answer
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

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

Show answer
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

Show answer
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

Show answer
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. $\displaystyle\sqrt{\frac{\mu _0}{\varepsilon}}$

Show answer
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)

Show answer
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.

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. $0.5m^{-1}$

Show answer
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

Show answer
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

Show answer
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

Show answer
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

Show answer
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

Show answer
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

Show answer
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

Show answer
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

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

Show answer
Correct Option: A

According to Maxwell's hypothesis, changing of electric filed give rise to

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

  1. magnetic field

  2. pressure gradient

  3. charge

  4. voltage

Show answer
Correct Option: A
Explanation:

According to Maxwell's hypothesis, changing of electric field gives rise to Magnetic field.

We know that $F=qE,$, where $F$ is force and $E$ is electric field.
We can relate magnetic field and force by $F=qvB$, where $v$ is velocity and $B$ is the magnetic field.
Therefore we can obtain magnetic field by changing electric field.
Therefore option $A$ is correct.

Unpolarized light falls first on polarizer $\left( P \right) $ and then on analyzer $\left( A \right) $. If the intensity of the transmitted light from the analyser is $\dfrac { 1 }{ 8 }$th of the incident unpolarized light. What will be the angle between optic axes of $P$ and $A$?

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

  1. ${ 45 }^{ o }$

  2. ${ 30 }^{ o }$

  3. Zero

  4. ${ 60 }^{ o }$

Show answer
Correct Option: D
Explanation:

Given,
$I=\dfrac { { I } _{ 0 } }{ 2 } $              ....(i)
${ I }^{ ' }=I\cos ^{ 2 }{ \theta  } $                 $\left( \because { I }^{ ' }=\dfrac { { I } _{ 0 } }{ 8 }  \right) $
$\therefore \dfrac { { I } _{ 0 } }{ 8 } =\dfrac { { I } _{ 0 } }{ 2 } \cos ^{ 2 }{ \theta  } $
From the equation (i), we have
$\dfrac { 1 }{ 4 } =\cos ^{ 2 }{ \theta  } \Rightarrow \cos { \theta  } ={ 1 }/{ 2 }$
$\Rightarrow \cos { \theta  } =\cos { { 60 }^{ o } } $
$\Rightarrow \theta ={ 60 }^{ o }$

A plane electromagnetic wave with an intensity of $200 W/m^2$ is incident normal to a flat plate of radius 30 cm. If the plate absorbs $60%$ and reflect $40%$ of the incident radiation, what is the momentum transferred to it in 5 min?

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

  1. $1.7 \times 10^{-3} kg ms^{-1}$

  2. $2.7 \times 10^{-4} kg ms^{-1}$

  3. $3.7 \times 10^{-4} kg ms^{-1}$

  4. $3.7 \times 10^{-3} kg ms^{-1}$

Show answer
Correct Option: A
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