25.1 ELECTROMAGNETIC VIBRATIONS
25.1.1 Electromagnetic (em) Waves
1 Production of electric and magnetic fields by accelerating charges
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Figure 25.1 The figure shows an electromagnetic wave consisting of an electric field (E) and a magnetic field (B) that are perpendicular to each other and also perpendicular to the direction of wave propagation. Both fields oscillate in phase and form sinusoidal waves as they travel through space. |
Consider a charge which is at rest. There is an electric field, but no magnetic field, surrounding it. The strength of the electric field does not change with time. Next, consider charges which undergo simple harmonic motion in a conductor. Now these charges accelerate, and consequently cause the strength of the electric field to change with time. This changing field can move away from the conductor by means of wave motion. As there is a current flowing in the conductor, a magnetic field is also produced. The strength of the field changes with time. The magnetic field too moves away from the conductor, together with the electric field. Hence, the acceleration of charges has produced both electric and magnetic fields which propagate away from the charges by means of wave motion through space at the speed of light.
2 Electric and magnetic wave motions
Suppose that we place a detector at a point at distance x from the charges accelerating in a conductor. As the charges accelerate, the detector can detect the presence of electric and magnetic fields at the point. These fields have the following features:
(a) The electric field and magnetic field are perpendicular to each other, as shown in Figure 25.1(a).
(b) The strength E of the electric field changes sinusoidally with time t. Its instantaneous value can be represented by the expression
E = E0 sin (ωt − kx)
where E0 is the maximum field strength, ω is the angular frequency of oscillation of the field strength and k is the wave number. The changing field strength E corresponds to the displacement y of a particle oscillating in a medium as mechanical wave passes by. For a harmonic mechanical wave, we have
y = y0 sin (ωt − kx)
Hence, the equation above is the wave equation representing progressive harmonic electric wave generated by the accelerating charges. Likewise, we have the equation
B = B0 sin (ωt − kx)
to represent the progressive harmonic magnetic wave.
(c) The two field strengths are in phase with each other. When E = 0, we will have B = 0 at the same instant.
(d) The direction of wave propagation is perpendicular to the wavefront of the electric waves and the magnetic waves. This means that em waves are transverse waves.
Figure 25.1(b) shows a graph of the field strength against distance x at a particular instant. Notice the following:
(a) If the E vector lies on the x–z plane, then the B vector must lie on the x–y plane.
(b) The direction of wave propagation is perpendicular to the E and B vectors.
(c) The wave profiles of both the electric and magnetic waves are sine curves.
25.1.2 Comparing EM Waves with Mechanical Waves
1 Em waves can propagate through vacuum but mechanical waves cannot.
2 Em waves are transverse waves whereas mechanical waves may be longitudinal or transverse.
3 Em waves originate from changing electric and magnetic fields whereas mechanical waves exist as a result of the oscillation of the particles of the medium through which the waves propagate.
25.2 RELATIONSHIP BETWEEN ε0, μ0 and c
25.2.1 Relationship between ε0, μ0 and c
1 The relationship
Using the set of Maxwell’s equations concerning electromagnetism, we can show theoretically that the speed c of electromagnetic waves in free space is given by
c = 1 / √(ε0 μ0)
where ε0 is the permittivity of free space
μ0 is the permeability of free space
2 Significance of the relationship
We have
ε0 = 8.854 × 10−12 F m−1 and μ0 = 4π × 10−7 N A−2
Hence, based on theory, the value of the speed of electromagnetic waves is
c = 1 / √(ε0 μ0)
= 1 / √[(8.854 × 10−12)(4π × 10−7)]
= 3.00 × 108 m s−1
We have measured experimentally the speed of light, and also get the value of 3.00 × 108 m s−1. This implies that light is propagated by transverse electromagnetic waves.
25.3 SPECTRUM OF ELECTROMAGNETIC WAVES
25.3.1 The Spectrum of Electromagnetic Waves
Electromagnetic waves have wavelengths ranging from a few metres to wavelengths of the order of 10−13 m. This wide range of wavelengths is known as the electromagnetic spectrum.
Owing to the fact that the properties of em waves in one small region of the spectrum differ greatly from those of em waves in another region, we normally divide the spectrum into several regions. The table below shows how the em spectrum is classified.
Spectrum of Electromagnetic Waves
Electromagnetic waves have wavelengths ranging from a few metres to about 10−13 m. This wide range is known as the electromagnetic spectrum and is classified into different regions based on frequency and wavelength.
| Types of Radiation | Sources | Frequency Range (Hz) | Wavelength Range (m) |
|---|---|---|---|
| Radio Waves | Electronic oscillators | 105 − 1010 | 10−2 − 103 |
| Microwaves | Magnetron tube | 109 − 1011 | 10−3 − 10−1 |
| Infrared | Hot objects | 1010 − 1014 | 10−7 − 10−2 |
| Visible Light | Incandescent objects, discharge tubes | 1015 | 10−7 |
| Ultraviolet | Electric arc | 1015 − 1017 | 10−7 − 10−9 |
| X-rays | X-ray tubes, high deceleration of charges | 1016 − 1018 | 10−10 − 10−8 |
| Gamma Rays | Nuclear radioactivity | 1018 − 1020 | 10−13 − 10−10 |
Applications of Electromagnetic Waves
Electromagnetic waves are widely used in modern technology and daily life. From communication systems to medical applications, EM waves play a crucial role in transmitting energy and information efficiently.
Radio Communication
Radio waves are used in broadcasting, television, and wireless communication systems to transmit signals over long distances.
Wireless Technology
Microwaves are used in Wi-Fi, mobile networks, and satellite communication to transfer data quickly and efficiently.
Heating & Infrared
Infrared radiation is used in heaters, thermal imaging cameras, and remote controls for detecting heat and energy.
Visible Light
Visible light allows human vision and is used in lighting systems, photography, and optical devices.
Ultraviolet Applications
Ultraviolet waves are used for sterilization, water purification, and detecting counterfeit materials.
Medical Imaging
X-rays are widely used in hospitals to examine bones and detect internal body conditions.
Gamma Rays
Gamma rays are used in cancer treatment (radiotherapy) and sterilization of medical equipment.
Why Electromagnetic Waves Are Important
Conclusion
Electromagnetic waves are fundamental to modern science and technology, playing a key role in communication, medical applications, and energy transfer. These waves consist of oscillating electric and magnetic fields that propagate through space at the speed of light.
Understanding the properties, wave equations, and electromagnetic spectrum allows us to see how different types of radiation—from radio waves to gamma rays—are applied in real life. Each region of the spectrum has unique characteristics and important uses in everyday technology.
In summary, electromagnetic waves are not only essential in physics but also form the backbone of modern innovations such as wireless communication, medical imaging, and advanced scientific research.
Frequently Asked Questions (FAQ)
Electromagnetic waves are waves made of oscillating electric and magnetic fields that travel through space at the speed of light.
No, electromagnetic waves can travel through a vacuum, unlike mechanical waves which require a medium.
The speed of electromagnetic waves in vacuum is approximately 3.00 × 108 m/s, also known as the speed of light.
Electromagnetic waves are transverse waves because their electric and magnetic fields oscillate perpendicular to the direction of propagation.
The electromagnetic spectrum is the range of all electromagnetic waves arranged by frequency or wavelength, from radio waves to gamma rays.
Examples include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
The wave equation can be written as E = E₀ sin(ωt − kx) and B = B₀ sin(ωt − kx).
They are produced by accelerating electric charges, which generate changing electric and magnetic fields.
The electric and magnetic fields are perpendicular to each other and oscillate in phase as the wave propagates.
They are used in communication systems, medical imaging, heating, wireless technology, and many modern technologies.
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