Electromagnetic Waves Test

Result

Electromagnetic Waves Test - 35

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Question 1
1 / -0

A plane electromagnetic wave in a non magnetic dielectric medium is given by $$\bar{E} = \bar{E_0} ( 4 \times 10^{-7}x - 50 t)$$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

A
5.8

B
2.4

C
1.6

D
3.5

Solution

Given equation of wave
$$\vec { E } =\vec { { E }_{ 0 } } \left( 4\times { 10 }^{ -7 }x-50t \right) $$
comparing with general equation of wave
$$\vec { E } =\vec { { E }_{ 0 } } \left( kx-\omega t \right) $$
we get
$$\omega =50rad/s;k=4\times { 10 }^{ -7 }{ m }^{ -1 }$$
Thus velocity of wave
$$V=\cfrac { \omega }{ k } =\cfrac { 50 }{ 4\times { 10 }^{ -7 } } =1.25\times { 10 }^{ 8 }m/s$$
So, refractive index of medium
$$\mu =\cfrac { e }{ V } =\cfrac { 3\times { 10 }^{ 8 } }{ 1.25\times { 10 }^{ 8 } } =2.4$$
using
$${ \mu }^{ 2 }=km.ke$$ ($$km$$ and $$ke$$ are di-magnetic and dielectric constants)
as medium is non diamagnetic, $$km=1$$
$$\Rightarrow ke={ \mu }^{ 2 }={ (2.4) }^{ 2 }\Rightarrow ke=5.76$$=5.8
Question 2
1 / -0

The mathematical equation for magnetic field lines of force is

A
$$\vec \nabla . \vec B = 0$$

B
$$\vec \Delta . \vec B \neq 0 1$$

C
$$\vec \nabla . \vec B > 0$$

D
$$\vec \nabla . \vec B < 0$$

Solution
Question 3
1 / -0

The magnetic field in a plane EM wave is given by - $$\mathrm { B } = ( 100 \mu \mathrm { T } ) \sin \left[ \left( 2 \times 10 ^ { 15 } \mathrm { S } ^ { - 1 } \right) ( \mathrm { t } - \mathrm { x } / \mathrm { c } ) \right] \hat { \mathrm { j } }$$
The equation for electric field is

A
$$\mathrm { E } = 100 \mu \mathrm { N } / \mathrm { C } \sin \left[ \left( 2 \times 10 ^ { 15 } \mathrm { s } ^ { - 1 } \right) ( \mathrm { t } - \mathrm { x } / \mathrm { c } ) \right] ( - \hat { \mathrm { k } } )$$

B
$$\mathrm { E } = 3 \times 10 ^ { 10 } \mu \mathrm { N } / \mathrm { Csin } \left[ \left( 2 \times 10 ^ { 15 } \mathrm { s } ^ { - 1 } \right) ( \mathrm { t } - \mathrm { x } / \mathrm { c } ) \right] ( - \hat { \mathrm { k } } )$$

C
$$\mathrm { E } = 3 \times 10 ^ { 10 } \mu \mathrm { N } / \mathrm { C } \sin \left[ \left( 2 \times 10 ^ { 15 } \mathrm { s } ^ { - 1 } \right) ( \mathrm { t } - \mathrm { x } / \mathrm { c } ) \right] \hat { \mathrm { k } }$$

D
$$\mathrm { E } = 100 \mu \mathrm { N } / \mathrm { C } \sin \left[ \left( 2 \times 10 ^ { 15 } \mathrm { s } ^ { - 1 } \right) ( \mathrm { t } - \mathrm { x } / \mathrm { c } ) \right] \mathrm { \hat k }$$

Solution
Question 4
1 / -0

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

A
Faraday's law of induction

B
Modified Ampere's law

C
Gauss's law of electricity

D
Gauss's law of magnetism

Solution
Question 5
1 / -0

On photo-emissive cell, with exciting wavelength I, the fastest electron has speed u. If the exciting wavelength is changed to 3I/4, the speed of the fastest emitted electron will be:

A
$$ u(3/4)^{ \frac { 1 }{ 2 } } $$

B
$$ u(4/3)^{ \frac { 1 }{ 2 } } $$

C
less than $$ u(4/3)^{ \frac { 1 }{ 2 } } $$

D
Greater than $$ u(4/3)^{ \frac { 1 }{ 2 } } $$

Solution
Question 6
1 / -0

An electro magnetic wave of frequency 3 MHz passes from Vacuum into a dielectric medium with permittivity $$ \epsilon = 4.0 $$ Then

A
Wave length doubled and frequency remains unchanged

B
Wave length doubled and frequency becomes half

C
Wave length is halved and frequency remains unchanged

D
Wave length and and frequency both remain unchanged

Solution
Question 7
1 / -0

In an electromagnetic wave in vacuum. The electrical and magnetic fields are $$40 \pi\ V/m$$ and $$0.4\times 10^{-7}T$$. The pointing vector

A
$$4.4\ Wm^{-1}$$

B
$$0.44\ Wm^{-1}$$

C
$$5.65\ Wm^{-1}$$

D
$$4.0\ Wm^{-1}$$

Solution
Question 8
1 / -0

Wavelength of light in different media are proportional to:

A
speed of light in that medium

B
Amplitude of light in that medium

C
frequency of light in that mrdium

D
Nove of above

Solution
Question 9
1 / -0

Which of the following electromagnetic waves have minimum frequency

A
Microwaves

B
Audible waves

C
Ultriasonic waves

D
Radiowaves

Solution
Question 10
1 / -0

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $$2 \times 10 ^ { 10 } \mathrm { Hz }$$ and amplitude 48V/m. The amplitude of oscillating magnetic field will be

A
$$\frac { 1 } { 16 } \times 10 ^ { - 8 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$$

B
$$16 \times 10 ^ { - 8 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$$

C
$$12 \times 10 ^ { - 7 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$$

D
$$\frac { 1 } { 12 } \times 10 ^ { - 7 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$$

Solution