Electromagnetic Waves Test

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Electromagnetic Waves Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

The oscillating electric and magnetic vectors of an electromagnetic wave are oriented along

A
The same direction but differ in phase by $$90^o$$

B
The same direction and are in phase

C
Mutually perpendicular directions and are in phase

D
Mutually perpendicular directions and differ in phase by $$90^o$$

Solution

$$\vec E$$ and $$\vec B$$ are mutually perpendicular to each other and are in phase i.e., they become zero and minimum at the same place and at the same time.
Question 2
1 / -0

A parallel plate capacitor with plate are $$A$$ and seperation between the plates $$d,$$ is charged byb a constant current $$i,$$ consider a plane surface of area $$A/2$$ parallel to the plates and drawn symmetrically between the plates, the displacement current through this area, will be.

A
$$i$$

B
$$\dfrac{i}{2}$$

C
$$\dfrac{i}{4}$$

D
None of these

Solution

Suppose the charge on the capacitor at time $$t$$ is $$Q,$$ the electric field between the plates of the capacitor is $$E=\dfrac{Q}{\varepsilon_{0}A}.$$ The flux through the area considered is $$\phi_{E}=\dfrac{Q}{\varepsilon_{0}A}\dfrac{A}{2}=\dfrac{Q}{2\varepsilon_{0}}$$
$$\therefore $$ the displacement current
$$i_{d}=\varepsilon_{0}\dfrac{d\phi_{E}}{dt}=\varepsilon_{0}\left(\dfrac{1}{2\varepsilon_{0}}\right)\dfrac{dQ}{dt}=\dfrac{i}{2}.$$
Question 3
1 / -0

If $$\vec{E}$$ and $$\vec{B}$$ are electric and magnetic field vectors of electromagnetic waves, then the propagation of electronic wave is along

A
$$\vec{E}$$

B
$$\vec{B}$$

C
$$\vec{E}\times \vec{B}$$

D
$$\vec{E}$$ . $$\vec{B}$$

Solution

Direction of Propagation of wave is perpendicular to both E and B vector.
Question 4
1 / -0

The figure here gives the electric field of an $$EM$$ wave at a certain poiunt and a certain instrant. the wave is transporting energy in the negative $$z$$ direction. what is tha direction of the magnetic field of the wave at that point and instant.

A
Towards + $$X$$ direction

B
Towards - $$X$$ direction

C
Towards + $$Z$$ direction

D
Towards - $$Z$$ direction

Solution

The direction of $$EM$$ wave is given by the direction of $$\vec{E}\times \vec{B}$$
Hence option a is the correct option.
Question 5
1 / -0

A typical microwave oven operates at a frequency of $$2.45 \,GHz$$. What is the wavelength associated with the electromagnetic waves in the oven?

A
$$8.20 \,m$$

B
$$12.2 \,cm$$

C
$$1.20 \times 10^8 \,m$$

D
$$8.20 \times 10^{-9} \,m$$

E
none of those answers

Solution

Frequency, wavelength, and the speed of light are related:
$$f\lambda=c \rightarrow \lambda=\dfrac{c}{f}=\dfrac{3.00\times10^8 \,m/s}{2.45\times 10^{9} \,Hz}=0.122 \,m=12.2 \,cm$$
Question 6
1 / -0

A plane electromagnetic wave with a single frequency moves in vacuum in the positive $$x$$ direction. Its amplitude is uniform over the $$yz$$ plane its wavelength,

A
increase

B
decrease

C
same

D
none

Solution

The same amount of energy passes through equal areas parallel to the $$yz$$ plane as the wave travels in the $$+x$$ direction, so the amplitude and the intensity, which is proportional to the square of the amplitude, do not change.
Question 7
1 / -0

A plane electromagnetic wave with a single frequency moves in vacuum in the positive $$x$$ direction. Its amplitude is uniform over the $$yz$$ plane.As the wave moves, does its frequency

A
increase

B
decrease

C
stay constant

D
none

Solution

The same amount of energy passes through equal areas parallel to the $$yz$$ plane as the wave travels in the $$+x$$ direction, so the amplitude and the intensity, which is proportional to the square of the amplitude, do not change and also frequency is the property of source so it will be remain same.
Question 8
1 / -0

A plane electromagnetic wave with a single frequency moves in vacuum in the positive $$x$$ direction. Its amplitude is uniform over the $$yz$$ plane. the amplitude of its magnetic field.

A
increase

B
decrease

C
same

D
none

Solution

The same amount of energy passes through equal areas parallel to the $$yz$$ plane as the wave travels in the $$+x$$ direction, so the amplitude and the intensity, which is proportional to the square of the amplitude, do not change.
Question 9
1 / -0

A plane electromagnetic wave with a single frequency moves in vacuum in the positive x direction. Its amplitude is uniform over the yz plane. its speed,

A
increase

B
decrease

C
stay constant

D
None of these

Solution

The same amount of energy passes through equal areas parallel to the $$yz$$ plane as the wave travels in the $$+x$$ direction, so the amplitude and the intensity, which is proportional to the square of the amplitude, do not change.
Question 10
1 / -0

Consider an electromagnetic wave traveling in the positive $$y$$ direction. The magnetic field associated with the wave at some location at some instant points in the negative $$x$$ direction as shown in Figure. What is the direction of the electric field at this position and at this instant?

A
the positive $$x$$ direction

B
the positive $$y$$ direction

C
the positive $$z$$ direction

D
the negative $$z$$ direction

E
the negative $$y$$ direction

Solution

An electromagnetic wave travels in the direction of the Poynting vector: $$\overrightarrow{S}=\overrightarrow{E}\times\overrightarrow{B}/\mu_0$$.

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Re-Attempt Weekly Quiz Competition

Electromagnetic Waves Test - 32

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Electromagnetic Waves Test - 32

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Question 1

The same direction but differ in phase by $$90^o$$

The same direction and are in phase

Mutually perpendicular directions and are in phase

Mutually perpendicular directions and differ in phase by $$90^o$$

Solution

Question 2

$$i$$

$$\dfrac{i}{2}$$

$$\dfrac{i}{4}$$

None of these

Solution

Question 3

$$\vec{E}$$

$$\vec{B}$$

$$\vec{E}\times \vec{B}$$

$$\vec{E}$$ . $$\vec{B}$$

Solution

Question 4

Towards + $$X$$ direction

Towards - $$X$$ direction

Towards + $$Z$$ direction

Towards - $$Z$$ direction

Solution

Question 5

$$8.20 \,m$$

$$12.2 \,cm$$

$$1.20 \times 10^8 \,m$$

$$8.20 \times 10^{-9} \,m$$

none of those answers

Solution

Question 6

increase

decrease

same

none

Solution

Question 7

increase

decrease

stay constant

none

Solution

Question 8

increase

decrease

same

none

Solution

Question 9

increase

decrease

stay constant

None of these

Solution

Question 10

the positive $$x$$ direction

the positive $$y$$ direction

the positive $$z$$ direction

the negative $$z$$ direction

the negative $$y$$ direction

Solution

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