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Electromagnetic Waves

Electromagnetic Waves

Have you ever wondered about how electromagnetic waves are produced? Stationary charges produce electrostatic fields and charges in uniform motion produce magnetic fields. So what can be the sources of electromagnetic waves? Let’s find out.

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Sources of Electromagnetic Waves

To begin with, one of the most important results of Maxwell’s theory is that accelerated charges radiate electromagnetic waves. Understanding the proof of it is beyond our scope of study but we will approach it based on reasoning.

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Discussion

Let’s consider a charge oscillating at a particular frequency. Remember, an oscillating charge is an example of an accelerating charge. This charge produces an oscillating electric field which results in an oscillating magnetic field which in turn is the source of an electric field and so on.

In simple words, the oscillating electric and magnetic fields regenerate each other propagating the wave through space. The frequency of the electromagnetic wave equals that of the oscillation of the charge. The energy required to propagate the wave through space comes at the expense of the accelerated charge.

The first logical thought is that it will be easy to test the prediction that light is an electromagnetic wave. Right? After all, we merely need to set up an AC circuit in which the current oscillates at the frequency of visible light, like the yellow light. However, that is simply not possible. Here’s why:

  • The frequency of yellow light is around 6 x 1014
  • The frequency available with most modern electronic circuits is around 1011

Hence, the experimental demonstration of electromagnetic waves can happen only in the low-frequency region (radio wave region). This was done by Hertz in an experiment in 1887.

Nature of the Electromagnetic Waves

From Maxwell’s equations you can observe that in an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation.

electromagnetic waves

Fig.1

In the figure above, you can see that the direction of the electric field inside the plates of the capacitor is perpendicular to the plates. This causes a displacement current and gives rise to a magnetic field along the perimeter of a circle parallel to the capacitor plates. So, B and E are perpendicular to each other.

Now, let’s look at a typical example of a plane electromagnetic wave propagating along the z-axis.

electromagnetic waves

Fig.2

In the figure above,

  • The electric field (Ex) is along the x-axis and varies sinusoidally with z at a given time.
  • The magnetic field (By) is along the y-axis and also varies sinusoidally with z.
  • Ex and By are perpendicular to each other and to the direction of propagation (z).

Mathematically,

Ex = E0 sin (kz–ωt)

By = B0 sin (kz–ωt)

Where magnitude of the wave vector (or propagation vector) k = 2π/λ … (λ is the wavelength of the wave) and ω is the angular frequency. The direction of k determines the direction of propagation of the wave. Now, you have already learned last year that

ω = ck, where, c = 1/ √μ0ε0

This relation is often written in terms of frequency, ν (=ω/2π) and wavelength, λ (=2π/k) as

2πv = c(2π/λ)

Or, vλ = c

According to Maxwell’s equations, the magnitude of electric and magnetic fields have the relation,

B0 = E0/c

Remarks

  • Electromagnetic waves are self-sustaining oscillations in free space/vacuum.
  • No material medium is involved in the vibrations of the fields

In the nineteenth century, scientists believed that there must be a medium across all space and matter. Also, this medium responds to electric and magnetic fields. They named this medium ether. However, in 1887 Michelson and Morley conducted an experiment conclusively demolishing the concept of ether. According to their observations, electric and magnetic fields can sustain each other even in a vacuum.

What if they were wrong?

We know that light, which is an electromagnetic wave, propagates through a glass. We also know that the total electric and magnetic fields inside a medium are described in terms of permittivity ε and a magnetic permeability μ. Replacing ε0 and μ0 in Maxwell’s equations with ε and μ of the material medium, we can calculate the velocity of light in that medium:

ν = 1/√με

Hence, the velocity of light depends on the electric and magnetic properties of the medium through which it travels. Various experiments have shown that the velocity of electromagnetic waves of different wavelengths is the same. The variation is up to a few meters per second out of a value of 3×108 m/s. There is a strong experimental support for this constant.

Electromagnetic waves travel with the speed of light

In his experiments, Hertz also demonstrated that waves with wavelengths ten million times that of the light waves can be diffracted, refracted and polarised. This establishes the wave nature of radiation. He also produced electromagnetic waves and determined their wavelengths by measuring the distance between two successive nodes.

Also, since the frequency of the wave was known (= frequency of the oscillator), he calculated the speed of the wave using the formula v= νλ. He found that the waves travelled with the same speed as the speed of light.

Do electromagnetic waves carry energy and momentum like other waves?

Simple answer – YES.

We know that in a region of free space with electric field E, the energy density is ε0E2/2. Also, the magnetic density associated with a magnetic field is B2/2μ0. Hence, an electromagnetic wave always has a non-zero density associated with it.

In Fig.2 above, consider a plane perpendicular to the direction of propagation of the electromagnetic wave. If there are electric charges on this plane, then they will be set and sustained in motion by the electric and magnetic fields of the wave.

Hence, they acquire energy and momentum like any other waves.

Further, the presence of momentum indicates that the wave also exerts pressure called radiation pressure. If the total energy transferred to a surface in time‘t’ is ‘U’, then the magnitude of the total momentum delivered to the surface for complete absorption is,

p = U/c

In 1903, Nicols and Hull verified this equation by measuring the radiation pressure of visible light. It is of the order of 7 x 10-6 N/m2. The great technological importance of electromagnetic waves stems from their capability to carry energy from one place to another.

Solved Examples for You

Question: Which of the following produces electromagnetic waves?

  1. Stationary charges
  2. Charges in uniform motion
  3. Accelerating charges
  4. None of the above

Solution: (c) – Accelerating charges. We know that stationary charges produce electrostatic fields and charges in uniform motion produce magnetic fields. Maxwell’s theory proves that accelerating charges produce electromagnetic waves.

Question: Why is it not possible to demonstrate electromagnetic waves in visible light?

Solution:  To demonstrate electromagnetic waves in visible light (like yellow light), one needs to set up an AC circuit in which the current oscillates with the frequency of the visible light. However, the frequency of yellow light is much higher than the frequency available with the most modern electronic circuits. Hence, it is not possible to demonstrate it in visible light.

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