###### Advertisements

###### Advertisements

Suppose that the electric field amplitude of an electromagnetic wave is E_{0} = 120 N/C and that its frequency is v = 50.0 MHz.

**(a)** Determine, B_{0}, ω, k, and λ.

**(b)** Find expressions for E and B.

###### Advertisements

#### Solution

Electric field amplitude, E_{0} = 120 N/C

Frequency of source, v = 50.0 MHz = 50 × 10^{6 }Hz

Speed of light, c = 3 × 10^{8 }m/s

**(a)** Magnitude of magnetic field strength is given as:

`"B"_0 = "E"_0/"c"`

= `120/(3 xx 10^8)`

= 4 × 10^{−7 }T

= 400 nT

Angular frequency of source is given as:

ω = 2πv

= 2π × 50 × 10^{6}

= 3.14 × 10^{8} rad/s

Propagation constant is given as:

`"k" = ω/"c"`

= `(3.14 xx 10^8)/(3 xx 10^8)`

= 1.05 rad/m

Wavelength of wave is given as:

`lambda = "c"/"v"`

= `(3 xx 10^8)/(50 xx 10^6)`

= 6.0 m

**(b)** Suppose the wave is propagating in the positive x-direction. Then, the electric field vector will be in the positive y-direction and the magnetic field vector will be in the positive z-direction. This is because all three vectors are mutually perpendicular.

Equation of electric field vector is given as:

`vec"E" = "E"_0 sin ("k""x" - ω"t")hat"j"`

= `120 sin [1.05"x" - 3.14 xx 10^8"t"]hat"j"`

And, magnetic field vector is given as:

`vec"B" = "B"_0 sin ("kx" - ω"t")hat"k"`

`vec"B" = (4 xx 10^-7) sin [1.05"x" - 3.14 xx 10^8"t"]hat"k"`

#### APPEARS IN

#### RELATED QUESTIONS

When Sunita, a class XII student, came to know that her parents are planning to rent out the top floor of their house to a mobile company she protested. She tried hard to convince her parents that this move would be a health hazard.

Ultimately her parents agreed :

(1) In what way can the setting up of transmission tower by a mobile company in a residential colony prove to be injurious to health?

(2) By objecting to this move of her parents, what value did Sunita display?

(3) Estimate the range of e.m. waves which can be transmitted by an antenna of height 20 m. (Given radius of the earth = 6400 km)

A charged particle oscillates about its mean equilibrium position with a frequency of 10^{9 }Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

In the study of a photoelectric effect the graph between the stopping potential V and frequency *v* of the incident radiation on two different metals P and Q is shown below:

(i) Which one of the two metals has higher threshold frequency?

(ii) Determine the work function of the metal which has greater value.

(iii) Find the maximum kinetic energy of electron emitted by light of frequency 8 × 10^{14} Hz for this metal.

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?

Write the expression for speed of electromagnetic waves in a medium of electrical permittivity ε and magnetic permeability μ.

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.

Can an electromagnetic wave be deflected by an electric field or a magnetic field?

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

A capacitor is connected to an alternating-current source. Is there a magnetic field between the plates?

Can an electromagnetic wave be polarised?

A plane electromagnetic wave is passing through a region. Consider (a) electric field (b) magnetic field (c) electrical energy in a small volume and (d) magnetic energy in a small volume. Construct the pairs of the quantities that oscillate with equal frequencies.

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

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.

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.

Which of the following is false for electromagnetic waves.

The electric and magnetic fields, associated with an electromagnetic wave, propagating along negative X-axis can be represented by ______.

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:

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

Why are e.m. waves non-mechanical?

Write a short note on the microwave.

Write down the properties of electromagnetic waves.

A pulse of light of duration 10^{-6} s is absorbed completely by a small object initially at rest. If the power of the pulse is 60 x 10^{-3} W, calculate the final momentum of the object.

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.

If the relative permeability and relative permittivity of the medium is 1.0 and 2.25, respectively. Find the speed of the electromagnetic wave in this medium.

Wavelength λ and wave vector k are related by ______.

In plane electromagnetic wave propagation velocity v, wavelength λ and frequency ν are related by ______.

The speed of plane electromagnetic waves is maximum in ______.

A man standing on the road has to hold his umbrella at 30° with the vertical to keep the rain away. He throws away the umbrella and starts, running at 10 km/h and finds raindrops hitting his head vertically. The speed of the raindrops with respect to the road is ______.

In space communication, the sound waves can be sent from one place to another

A plane electromagnetic wave travels in free space along x-axis. At a particular point in space, the electric field along y-axis is 9.3 Vm^{−1}. The magnetic induction (B) along z-axis is:

Dimensions of 1/(µOE_{0}) is

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?

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 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`.

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 ______.

A plane electromagnetic wave, has frequency of 2.0 × 10^{10} Hz and its energy density is 1.02 × 10^{-8} J/m^{3} in vacuum. The amplitude of the magnetic field of the wave is close to `(1/(4piepsilon_0) = 9xx10^9"Nm"^2/"C"^2 "and speed of light" = 3 xx 10^8 "m" "s"^-1)`:

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})

A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x × 10^{-8 }T. The value of x is ______.

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 ______.

An electromagnetic wave is produced by a charge ______.

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