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Electromagnetic Waves

Last Updated : 03 Mar, 2022
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A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities that is commonly described by a wave equation in physics, mathematics, and related subjects. Electromagnetic waves are a mix of electric and magnetic field waves produced by moving charges. The origin of all electromagnetic waves is a charged particle. This charged particle generates an electric field (which can exert a force on other nearby charged particles). When a charged particle accelerates as part of an oscillatory motion (as predicted by Maxwell’s equations), it causes ripples, or oscillations, in its electric field, as well as a magnetic field. Let’s take a closer look. The concept of electromagnetic waves!

What are Electromagnetic Waves?

Electromagnetic (EM) waves are waves that are related to both electricity and magnetism. These waves travel over space and are made up of time-varying electric and magnetic fields.

When electric and magnetic fields interact and change over time, electromagnetic waves are produced. These waves, which are linked to electricity and magnetism, would almost certainly travel beyond space.

The electromagnetic equations are derived using Maxwell’s equations. These EM waves, according to Maxwell, have a wide range of unique properties that can be applied to a variety of purposes. Electromagnetic waves are the connected temporally changing electric and magnetic fields that flow through space.

The magnetic field varies with time and gives rise to the electric field; the electric field changes with time and gives rise to the magnetic field again, and so on. When time-varying electric and magnetic fields are coupled and propagate together in space, electromagnetic waves are formed.

Electromagnetic Wave

The magnetic field, like the electric field, is a sine wave, except it goes in the opposite direction. Both of these fields (Electric and magnetic) generate electromagnetic fields. When the electric field is along the x-axis and the magnetic field is along the y-axis, the wave propagates on the z-axis. The propagation direction of waves and the electric and magnetic fields are perpendicular to each other.

Formation of Electromagnetic waves 

In general, a charged particle generates an electric field. Other charged particles are pushed by this electric field. Negative charges accelerate in the opposite direction of the field, while positive charges accelerate in the field’s direction. The magnetic field is created by a travelling charged particle. Other moving particles are pushed by this magnetic field. Because the force acting on these charges is always perpendicular to their motion, it only influences the velocity’s direction, not its speed.

As a result, the electromagnetic field is created by an accelerating charged particle. Electric and magnetic fields travelling at the speed of light c through open space are referred to as electromagnetic waves. A charged particle is considered to be accelerating when it oscillates about an equilibrium place. The charged particle produces an electromagnetic wave of frequency f if its oscillation frequency is f. This wave’s wavelength λ can be determined using the formula λ = c/f. Electromagnetic waves are a sort of space-based energy transfer.

Sources of Electromagnetic Wave (EM)

  • Electromagnetic waves are created when electrically charged particles vibrate. The vibration of the electric field associated with the speeding charge produces an oscillating magnetic field. These vibrating electric and magnetic fields produce electromagnetic waves.
  • When the charge is at rest, the electric field associated with it is also static. As a result, because the electric field does not change with time, no EM waves are generated.
  • A charge travelling at uniform velocity has no acceleration. Because the change in electric field with time is also constant, no electromagnetic waves would be generated. This illustrates that the only way to make EM waves is to accelerate charges.
  • Consider the instance of an oscillating charge particle. It has an oscillating electric field that creates an oscillating magnetic field. After then, the oscillating magnetic field generates an oscillating electric field, and so on.
  • The propagation of the wave = the regeneration of electric and magnetic fields.
  • All of these events are contained in an electromagnetic wave. It’s also worth noting that the frequency of an EM wave is always equal to that of the oscillating particle that produces it.

Nature of Electromagnetic waves

  • Transverse waves are Electromagnetic waves. The disturbance or displacement in the medium caused by transverse waves is perpendicular to the wave’s propagation direction. In such a wave, the medium particles travel in a path perpendicular to the wave’s propagation direction.
  • The electric and magnetic fields will be perpendicular to an EM wave propagating along the x-axis. When wave propagation is parallel to the x-axis, the electric field is parallel to the y-axis, and the magnetic field is parallel to the z-axis.
  • In nature, Electromagnetic waves are clearly transverse waves. The electric field of an EM wave is now provided by,

Ey = E0sin(kx-ωt )

where, Ey is the x-axis represents wave propagation, while the y-axis represents the electric field.

  • The following formula is used to compute the wavenumber-

k = (2π/ωt)

  • The magnetic field of an electromagnetic wave is created by,

Bz = B0sin( kx-ωt )

where, Bz is the electric field is along the z-axis, while the wave propagation direction is x.

B0 = (E0/c)

Here, we do some electromagnetic wave observations. In free space or vacuum, they’re self-sustaining electric and magnetic field oscillations. The electric and magnetic field vibrations are unlike any other waves we’ve looked at so far in that there is no material medium involved. Longitudinal compression and rarefaction waves are compressions and rarefaction waves in the air. A rigid, shear-resistant solid can also propagate transverse elastic (sound) waves. 

Energy of Electromagnetic waves

  • EM waves carry energy with them as they move. As a result of this feature, they have a wide range of uses in our daily lives. The energy of an EM wave is carried in part by an electric field and partly by a magnetic field.
  • The total energy stored per unit volume in an EM wave is calculated as,

ET = Per unit volume electric field energy is stored + stored magnetic field energy per unit volume

ET = (1/2)(E2ε0) + (1/2)(B2μ0)

  • Experimentally, it has been discovered that,

Speed of an EM wave = Speed of light

ET = (1/2)(E2ε0) + (1/2)(E2/c2μ0)

  • Maxwell’s equations-

ET = (1/2)(E2ε0) + (1/2)(E2μ0ε0)

ET = E2ε0

Mathematical Representation of Electromagnetic Wave 

It’s a plane we’re talking about. In the x-direction, the shape of an electromagnetic wave is

E(x , t) = Emax cos(kx – ωt + φ)

B(x , t) = Bmax cos(kx – ωt + φ)

where,

  • E = electric field vector in an electromagnetic wave,
  • B = magnetic field vector in an electromagnetic wave.

Maxwell was the first to envision electromagnetic radiations, while Hertz was the first to experimentally confirm the presence of an electromagnetic wave. The propagation direction of an electromagnetic wave is determined by the vector cross product of the electric and magnetic fields. It’s written like this:

\vec E\times\vec B

Characteristics of EM waves

  • The velocity of EM waves in open space or vacuum is a fundamental constant. In experiments, the velocity of EM waves was discovered to be the same as the speed of light. (c = 3 × 108 m/s). c is a basic constant defined as follows :

c = 1/√μ0ε0

  • EM waves require time-varying electric and magnetic fields to propagate. Electromagnetic waves convey both energy and velocity.
  • ET=E2ε0 is the total energy stored per unit volume in EM waves (Partly carried by an electric field and partly by magnetic field). This is a vital element for EM waves practical applications since they carry both energy and momentum.
  • EM waves are used in communication, such as in cell phone speech communication.
  • Electromagnetic waves (EM waves) apply pressure. Because they carry energy and momentum, they exert pressure. The force exerted by electromagnetic waves is known as radiation pressure.
  • The form of sunlight that we receive from the sun, for example, is visible light rays. These light beams are included in EM waves. Our hand will become warm and sweaty if we leave them in the sun for a long time. Because sunlight is transmitted in the form of energy-carrying electromagnetic waves (EM waves), this occurs.
  • Assume that the total energy transferred to the hand is equal to E. Momentum = (E/c) Because c is so huge, the momentum appears to be little. The pressure is also low because the momentum is so low. Because of this, our hands are not affected by the sun’s pressure.

Applications of Electromagnetic Waves

  1. These waves assist the pilot in navigating the aircraft and accomplishing a smooth take-off and landing. They’re also used to figure out how fast planes are flying.
  2. Radio and television broadcasting signals are transmitted via electromagnetic waves.
  3. In the medical field, these waves can be used in a variety of ways. X-rays and laser eye surgery, for example.
  4. They are utilized in electronic equipment like television remote controls, remote vehicles, LED televisions, microwave ovens, and so on.
  5. Electromagnetic waves can be used to determine the speed of passing cars.

Sample Questions 

Question 1: In free space, a planar electromagnetic wave with a frequency of 44 MHz moves in the x-direction. E = 7.3 \hat j  V/m at a specific point in space and time. At this moment, what is B?

Answer:

Given : E = 7.3 V/m, c = 3 × 108 m/s

We have,

B = E/c

 ∴ B = 7.3 / 3 × 108

 ∴ B = 2.433 × 108 T

We may determine the direction by noting that E is along the y-axis and the wave propagates along the x-axis. As a result, B should be perpendicular to both the x- and y-axes. E × B should be along the x-axis, according to vector algebra. B is in the z-direction because- 

(+\hat j ) × (+\vec k ) = (+\hat j)\times(+\hat k) =\hat i             .

Thus,

B = 2.433 \times 10^8 \hat k\text{ T}

Question 2: The magnetic field in a plane electromagnetic wave is given by By =(2 × 10-7)T sin (0.5 × 103x + 1.5 × 1011t). What are the wave’s wavelength and frequency?

Answer:

Comparing the given equation with

B = B0 sin[2π(x/λ + t/T)]

We have, 

λ = (2π/0.5×103) m = 1.26 cm.

And 1/T = ν = 1.5 × 1011)/2π = 23.9 GHz.

Question 3: At normal incidence, light with an energy flow of 18 W/cm2 falls on a non-reflecting surface. Find the average force applied on the surface over a 30-minute period if the surface has an area of 20 cm2.

Answer:

The total amount of energy that falls on the surface is

U = (18 W/cm2) × (20 cm2) × (30 × 60 s)

∴ U = 6.48 × 105 J

As a result, the total delivered momentum (for complete absorption) is

p =  U/c  

∴ p = 6.48 × 105 J / 3 × 108 m/s

∴ p = 2.16 × 10–3 kg m/s

The surface is subjected to an average force of

F = p/t

∴ F = 2.16 × 10-3 / 0.18 × 10

F = 1.2 × 10-6 N

Question 4: Write four applications of electromagnetic waves.

Answer:

Applications of electromagnetic waves :

  • We can see everything around us thanks to electromagnetic radiation.
  • These waves assist the pilot in navigating the aircraft and accomplishing a smooth take-off and landing. They’re also used to figure out how fast planes are flying.
  • In the medical field, these waves can be used in a variety of ways. X-rays and laser eye surgery, for example.
  • Radio and television broadcasting signals are transmitted via electromagnetic waves.

Question 5: Explain the formation of electromagnetic waves.

Answer:

In general, a charged particle generates an electric field. Other charged particles are pushed by this electric field. Negative charges accelerate in the opposite direction of the field, while positive charges accelerate in the field’s direction.

The magnetic field is created by a travelling charged particle. Other moving particles are pushed by this magnetic field. Because the force acting on these charges is always perpendicular to their motion, it only influences the velocity’s direction, not its speed.

As a result, the electromagnetic field is created by an accelerating charged particle. Electric and magnetic fields travelling at the speed of light c through open space are referred to as electromagnetic waves. A charged particle is considered to be accelerating when it oscillates about an equilibrium place. The charged particle produces an electromagnetic wave of frequency f if its oscillation frequency is f. This wave’s wavelength λ can be determined using the formula λ = c/f. Electromagnetic waves are a sort of space-based energy transfer.



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