###### Advertisements

###### Advertisements

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ______ × 10^{-2} cm.

#### Options

167

367

667

967

###### Advertisements

#### Solution

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be **667** × 10^{-2} cm.

**Explanation:**

Wavelength of EM wave λ_{v} in vacuum

= `"c"/"f"=(3xx10^8)/(3xx10^9)` = 0.1 m

∴ Wavelength of EM wave λ_{m} in medium = `0.1/mu`

Where µ is refractive index given by,

µ = `sqrt(mu_"r"epsilon_"r")`

Assuming material to be non-magnetic,

µ_{r} = 1

∴ µ = `sqrt(1xx2.25)` = 1.5

λ_{m }= `0.1/1.5 = 1/15`m

= 6.67 cm

= 667 × 10^{-2} cm.

#### RELATED QUESTIONS

How is the speed of em-waves in vacuum determined by the electric and magnetic field?

Do electromagnetic waves carry energy and momentum ?

What is the ratio of the speed of gamma rays to that of radio waves in a vacuum?

How are electric vector `(vec "E")`, magnetic vector `(vec "B")` and velocity vector `(vec "C")` oriented in an electromagnetic wave?

Why is the amount of the momentum transferred by the em waves incident on the surface so small ?

Arrange the following electromagnetic waves in decreasing order of wavelength:

Write the following radiations in ascending order with respect to their frequencies:

X-rays, microwaves, UV rays and radio waves.

How does a charge q oscillating at certain frequency produce electromagnetic waves?

Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave propagating along the Z-direction.

In a microwave oven, the food is kept in a plastic container and the microwaves is directed towards the food. The food is cooked without melting or igniting the plastic container. Explain.

A wire carries an alternating current i = i_{0} sin ωt. Is there an electric field in the vicinity of the wire?

An electromagnetic wave going through vacuum is described by

E = E_{0} sin (kx − ωt); B = B_{0} sin (kx − ωt).

Which of the following equations is true?

Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

(a) increases

(b) decreases

(c) does not change

(d) is zero

Speed of electromagnetic waves is the same

Which of the following have zero average value in a plane electromagnetic wave?

(a) Electric field

(b) Magnetic field

(c) Electric energy

(d) Magnetic energy

The energy contained in a small volume through which an electromagnetic wave is passing oscillates with

A point charge is moving along a straight line with a constant velocity v. Consider a small area A perpendicular to the motion of the charge. Calculate the displacement current through the area when its distance from the charge is x. The value of x is not large, so that the electric field at any instant is essentially given by Coulomb's law.

Consider the situation of the previous problem. Define displacement resistance R_{d} = V/i_{d}of the space between the plates, where V is the potential difference between the plates and i_{d} is the displacement current. Show that R_{d} varies with time as `R_d = R(e^(t"/"tau) - 1)` .

The energy associated with light of which of the following colours is minimum :

This is an example of step-up transformer .

Define frequency modulation and state any one advantage of frequency modulation (FM) over amplitude modulation (AM).

State any one property which is common to all electromagnetic waves.

The energy levels of an atom of a certain element are shown in the given figure. Which one of the transitions A, B, C, D or E will result in the emission of photons of electromagnetic radiation of wavelength 618.75 nm? Support your answer with mathematical calculations.

The dimension of `1/(mu_0 ∈_0)` is

Which of the following electromagnetic radiations is used for viewing objects through fog ______.

Which of the following is false for electromagnetic waves.

An e.m. wave is propagating in a medium with a velocity `vec"v" = "v" hat"i"`. The instantaneous oscillating electric field of this e.m. wave is along +y-axis, then the direction of an oscillating magnetic field of the e.m. wave will be along:

Which of the following is an electromagnetic wave?

What is displacement current?

Write down the integral form of modified Ampere’s circuital law.

Why are e.m. waves non-mechanical?

Write a short note on the visible spectrum.

Let an electromagnetic wave propagate along the x-direction, the magnetic field oscillates at a frequency of 10^{10} Hz and has an amplitude of 10^{-5} T, acting along the y – direction. Then, compute the wavelength of the wave. Also write down the expression for the electric field in this case.

Maxwell’s displacement current is a response to inconsistency in the ______.

The magnetic field of a plane electromagnetic wave travelling in +ve z-direction is described by ______.

Radio waves for FM radio have a frequency about ______.

Which one of the following does not represent simple harmonic motion? Here y denotes the instantaneous displacement. Here, A and B are constants and co is the angular frequency.

Dimensions of 1/(µOE_{0}) is

Which of the following electromagnetic radiations has the smallest wave length?

An accelerate electron would produce.

If a source is transmitting electromagnetic waves of frequency 8.2 × 10^{6} Hz. then wavelength of electromagnetic waves transmitted from the source will be.

The velocity of light in vacuum can be changed by changing

The velocity of electromagnetic wave is parallel to

Which of the following are not electromagnetic waves?

Dimensions of ε_{0} `(d phi_ε)/(dt)` are of

For which frequency of light, the eye is most sensitive?

Electromagnetic waves are produced by ______.

Which of the following type of radiations are radiated by an oscillating electric charge?

For a plane electromagnetic wave propagating in x-direction, which one of the following combinations gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

For a plane electromagnetic wave propagating in the x-direction, which one of the following combinations gives the correct possible directions for the electric field (E) and magnetic field (B) respectively?

A linearly polarized electromagnetic wave given as E = E_{o}î cos (kz – ωt) is incident normally on a perfectly reflecting infinite wall at z = a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as ______.

A charged particle oscillates about its mean equilibrium position with a frequency of 10^{9} Hz. The electromagnetic waves produced ______.

- will have frequency of 10
^{9}Hz. - will have frequency of 2 × 10
^{9}Hz. - will have a wavelength of 0.3 m.
- fall in the region of radiowaves.

A plane EM wave travelling along z direction is described by `E = E_0 sin (kz - ωt)hati` and `B = B_0 sin (kz - ωt)hatj`. show that

- The average energy density of the wave is given by `u_(av) = 1/4 ε_0E_0^2 + 1/4 B_0^2/mu_0`.
- The time averaged intensity of the wave is given by `I_(av) = 1/2 cε_0 E_0^2`.

The intensity of the light from a bulb incident on a surface is 0.22 W/m^{2} . The amplitude of the magnetic field in this light-wave is ______× 10^{–9 }T.

(**Given: **Permittivity of vacuum ε_{0} = 8.85 × 10^{–12} C^{2 }N^{–1} – m^{–2}, speed of light in vacuum c = 3 × 10^{8} ms^{-1})

A plane electromagnetic wave of frequency 500 MHz is travelling in a vacuum along a y-direction.

At a particular point in space and time, `vec"B"` = 8.0 × 10^{-8} `hat"Z"`T. The value of the electric field at this point is ______.

(speed of light = 3 × 10^{8} ms^{-1})

`hat x, hat y, hat z` are unit vectors along x, y, and Z directions.

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (U_{e}) and magnetic (U_{m}) fields is ______.

The electric field in a plane electromagnetic wave is given by `vecE = 200cos[((0.5 xx 10^3)/m)x - (1.5 xx 10^11 "rad"/s xx t)]V/mhatj`. If the wave falls normally on a perfectly reflecting surface having an area of 100 cm^{2}. If the radiation pressure exerted by the E.M. wave on the surface during a 10-minute exposure is `x/10^9 N/m^2`. Find the value of x.

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm^{-1} along the y-direction. Its corresponding magnetic field component, B would be ______.

Sunlight falls normally on a surface of area 36 cm^{2} and exerts an average force of 7.2 × 10^{-9} N within a time period of 20 minutes. Considering a case of complete absorption the energy flux of incident light is ______.

The electric field in an electromagnetic wave is given by E = 56.5 sin ω(t - x/c)Nc^{-1}. Find the intensity of the wave if it is propagating along x-axis in the free space.

(Given ε_{0} = 8.85 × 10^{-12} C^{2} N^{-1} m^{-2})

In a plane electromagnetic wave, the direction of electric field and magnetic field are represented by `hat"k"` and 2`hat"i" - 2hat"j"`, respectively. What is the unit vector along direction of propagation of the wave.

A 27 mW laser beam has a cross-sectional area of 10 mm^{2}. The magnitude of the maximum electric field in this electromagnetic wave is given by:

[Given permittivity of space ∈_{0} = 9 × 10^{-12} SI units, Speed of light c = 3 10^{8} m/s]

An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ∈ = 4.0. Then ______.

Name the electromagnetic wave/radiation which is used to study crystal structure.