Electromagnetic Waves Test

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Electromagnetic Waves Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

If the wavelength of red light in air is $$7500$$ $$\overset{o}{A}$$, then the frequency of light in air is ___________.

A
$$7.5\times 10^{10}$$Hz

B
$$3\times 10^{14}$$Hz

C
$$4\times 10^{14}$$Hz

D
$$5\times 10^{14}$$Hz

Solution

Velocity of wave $$=$$ wavelength X frequency
$$v=3\times { 10 }^{ 8 }m/s\\ \lambda =7500\overset { 0 }{ A } =7500\times { 10 }^{ -10 }m\\ f=\dfrac { 3\times { 10 }^{ 8 } }{ 7500\times { 10 }^{ -10 } } =4\times { 10 }^{ 14 }\ Hz$$
Question 2
1 / -0

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

A
Magnetic field is zero everywhere

B
Magnetic monopole cannot exist

C
Magnetic lines of force do not intersect each other

D
A current produces magnetic field

Solution

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.
Question 3
1 / -0

An electromagnetic wave going through vacuum is described by $$E=E_0\sin{(kx-\omega t)}$$; $$B=B_0\sin{(kx-\omega t)}$$.
Which of the following equation is true?

A
$$E_0k=B_0\omega$$

B
$$E_0\omega=B_0k$$

C
$$E_0B_0=\omega k$$

D
None of the above

Solution

$$\displaystyle\dfrac{E_0}{B_0}=c$$, also $$\displaystyle k=\dfrac{2\pi}{\lambda}$$ and $$\omega=2\pi v$$.

$$\implies \displaystyle\dfrac{E_0}{B_0} = \dfrac{\omega}{k}$$

$$E_0k=B_0\omega$$.
Question 4
1 / -0

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

A
Photoelectric effect

B
Compton effect

C
Raman effect

D
All of these
Solution
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.
Question 5
1 / -0

A parallel plate capacitor is charged to $$60 \mu C$$. Due to a radioactive source, the plate loses charge at the rate of $$1.8\times 10^{-8}C/s$$. The magnitude of displacement current is:

A
$$1.8\times 10^{-8}C/s$$

B
$$3.6\times 10^{-8}C/s$$

C
$$4.1\times 10^{-11}C/s$$

D
$$5.7\times 10^{-12}C/s$$

Solution

The displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.
Maxwell found that conduction current (I) and displacement current $$(I_{d})$$ together have the property of continuity, although individually they may not be continuous. Maxwell also predicted that this current produces the same magnetic field as a conduction current can produce.
Displacement current is given by
$$I_{d} = \dfrac {dq}{dt} = 1.8\times 10^{-8}C/s$$
Question 6
1 / -0

Assertion: Dipole oscillations produce electromagentic waves,
Reason : Accelerated charge produces electromagnetic waves

A
If both assertion and reason are true but the reason is the correct explanation of assertion.

B
If both assertion and reason are true but the reason is not the correct explanation of assertion.

C
If assertion is true but reason is false.

D
If both the assertion and reason are false.

E
If reason is true but assertion is false.

Solution

Hertz produced em waves by oscillating charge between dipolar electric field.
A charge moving with non-zero acceleration where both magnetic and electric field are varying emits em waves but this does not explain assertion.
Question 7
1 / -0

The electric field of an electromagnetic wave in free space is given by $$\vec E = 10cos (10^7 t + kx) \widehat{j } V/m,$$ where t and x are in seconds and metres respectively. It canbe inferred that
(a) The wavelength $$\lambda$$ is 188.4 m
(b) The wave number k is 0.33 rad/m
(c) The wave amplitude is 10 V/m
(d) The wave is propagating along +$$x$$ direction
Which one of the following pairs of statements is correct?

A
(a) and (b)

B
(b) and (c)

C
(a) and (c)

D
(c) and (d)

Solution

If $$E = A sin( +kx + \omega t)$$
then, wave propagation occurs in $$-x$$ direction.
Amplitude is $$A$$, wave number is $$k$$, wavelength is $$2 \pi/k$$ and wave velocity is $$\omega/k$$

Hence,
$$A= 10 V/m$$
$$c = \omega/k $$
$$3 \times 10^8 = 10^7/k$$
$$k = 0.033\ rad/m$$
$$\lambda = 2\pi/k = 60 \pi = 188.4 m$$
Question 8
1 / -0

The pressure exerted by an electromagnetic wave of intensity $$\displaystyle I\left( { watt }/{ { m }^{ 2 } } \right) $$ on a non-reflecting surface is : [c is the velocity of light]

A
$$\displaystyle Ic$$

B
$$\displaystyle { Ic }^{ 2 }$$

C
$$\displaystyle { I }/{ c }$$

D
$$\displaystyle { I }/{ { c }^{ 2 } }$$

Solution

Momentum of a photon
$$\displaystyle =\frac { h }{ \lambda } =\frac { h }{ { c }/{ v } } =\frac { hv }{ c } =\frac { E }{ c } $$
Momentum over unit area
$$\displaystyle =\frac { E }{ Ac } =\frac { I }{ c } \left[ I=\frac { E }{ A } for\quad wave \right] $$
Since surface is non reflecting, final momentum of photon = 0, change in momentum $$\displaystyle =\frac { I }{ c } $$
So, force per unit area $$\displaystyle =\frac { I }{ c } $$
Pressure of radiation $$\displaystyle =\frac { I }{ c } $$
Question 9
1 / -0

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

A
parallel to each other

B
perpendicular to each other

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

D
none of these

Solution

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.
Question 10
1 / -0

The electric field for an electromagnetic wave in free space is $$\vec{E}=\vec{i}30\cos(kz-5\times 10^8t)$$, where magnitude of $$\vec E$$ is in $$V/m$$. The magnitude of wave vector, $$k$$ is:
(velocity of em wave in free space $$=3\times 10^8m/s$$)

A
$$0.46$$ $$rad\ m^{-1}$$

B
$$3$$ $$rad\ m^{-1}$$

C
$$1.66$$ $$rad\ m^{-1}$$

D
$$0.83$$ $$rad\ m^{-1}$$

Solution

Electric field of an EM wave $$\vec{E} =30 (kz - 5\times 10^8 t) \hat{i}$$
$$\implies$$ $$\omega = 5\times 10^8$$ rad/s
Given : Velocity of EM wave $$v = 3\times 10^8$$ $$m/s$$
Using $$v = \dfrac{w}{k}$$ $$\implies k = \dfrac{w}{v}$$

$$\therefore$$ $$k = \dfrac{5\times 10^8}{3\times 10^8} = 1.66$$ rad $$m^{-1}$$

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Electromagnetic Waves Test - 20

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Question 1

$$7.5\times 10^{10}$$Hz

$$3\times 10^{14}$$Hz

$$4\times 10^{14}$$Hz

$$5\times 10^{14}$$Hz

Solution

Question 2

Magnetic field is zero everywhere

Magnetic monopole cannot exist

Magnetic lines of force do not intersect each other

A current produces magnetic field

Solution

Question 3

$$E_0k=B_0\omega$$

$$E_0\omega=B_0k$$

$$E_0B_0=\omega k$$

None of the above

Solution

Question 4

Photoelectric effect

Compton effect

Raman effect

All of these

Solution

Question 5

$$1.8\times 10^{-8}C/s$$

$$3.6\times 10^{-8}C/s$$

$$4.1\times 10^{-11}C/s$$

$$5.7\times 10^{-12}C/s$$

Solution

Question 6

If both assertion and reason are true but the reason is the correct explanation of assertion.

If both assertion and reason are true but the reason is not the correct explanation of assertion.

If assertion is true but reason is false.

If both the assertion and reason are false.

If reason is true but assertion is false.

Solution

Question 7

(a) and (b)

(b) and (c)

(a) and (c)

(c) and (d)

Solution

Question 8

$$\displaystyle Ic$$

$$\displaystyle { Ic }^{ 2 }$$

$$\displaystyle { I }/{ c }$$

$$\displaystyle { I }/{ { c }^{ 2 } }$$

Solution

Question 9

parallel to each other

perpendicular to each other

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

none of these

Solution

Question 10

$$0.46$$ $$rad\ m^{-1}$$

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

$$1.66$$ $$rad\ m^{-1}$$

$$0.83$$ $$rad\ m^{-1}$$

Solution

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