Revision of EM waves class 12
Electromagnetic Waves – Class 12 Physics: Complete Notes, Important Formulas & Concepts
Electromagnetic Waves is an important chapter of Class 12 Physics. It is comparatively short, but it contains several important concepts and direct formula-based questions that are frequently useful for CBSE board examinations.
In this chapter, we study how changing electric and magnetic fields can travel through space in the form of waves. We also learn about Maxwell’s displacement current, the properties of electromagnetic waves and the complete electromagnetic spectrum, from radio waves to gamma rays.
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1. What are Electromagnetic Waves?
Electromagnetic waves are waves consisting of oscillating electric and magnetic fields that propagate through space.
An electromagnetic wave contains:
– An oscillating electric field (E)
– An oscillating magnetic field (B)
– A direction of propagation
The electric field and magnetic field are mutually perpendicular and both are perpendicular to the direction in which the wave travels.
Therefore:
E ⟂ B ⟂ Direction of propagation
This is why electromagnetic waves are called transverse waves.
Unlike mechanical waves such as sound waves, electromagnetic waves do not require a material medium for propagation. They can travel through vacuum.
Examples of electromagnetic waves include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.
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2. Maxwell’s Electromagnetic Theory
James Clerk Maxwell theoretically predicted the existence of electromagnetic waves.
According to Maxwell, a changing electric field produces a magnetic field and a changing magnetic field produces an electric field.
These continuously changing electric and magnetic fields sustain each other and propagate through space as an electromagnetic wave.
Maxwell also showed that the speed of electromagnetic waves in vacuum is:
c = 1 / √(μ₀ε₀)
where:
– c = speed of electromagnetic waves in vacuum
– μ₀ = permeability of free space
– ε₀ = permittivity of free space
The calculated value is:
c ≈ 3 × 10⁸ m/s
This was equal to the known speed of light. Maxwell therefore concluded that light itself is an electromagnetic wave.
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3. Displacement Current
One of the most important concepts introduced by Maxwell is displacement current.
Consider a capacitor being charged. Current flows through the wires connected to the capacitor, but no actual charge flows across the insulating gap between its plates.
However, there is a changing electric field between the plates.
Maxwell proposed that this changing electric field produces an effect equivalent to current, which he called displacement current.
The formula for displacement current is:
Iᵈ = ε₀ × dΦᴇ/dt
where:
– Iᵈ = displacement current
– ε₀ = permittivity of free space
– Φᴇ = electric flux
Electric flux is given by:
Φᴇ = E A cos θ
For a charging capacitor, the displacement current is equal to the conduction current:
Iᵈ = I
This concept was essential for Maxwell’s theory of electromagnetic waves.
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4. How are Electromagnetic Waves Produced?
Electromagnetic waves are produced by accelerating charges.
A stationary charge produces an electric field. A moving charge produces electric and magnetic fields, but an accelerating or oscillating charge produces electromagnetic radiation.
For example, in a transmitting antenna, alternating current causes electrons to oscillate rapidly. The changing electric and magnetic fields produced by these oscillating charges travel outward in the form of electromagnetic waves.
Therefore, remember:
Accelerating charge → Electromagnetic radiation
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5. Nature of Electromagnetic Waves
The important properties of electromagnetic waves are:
1. They are transverse waves
The electric field, magnetic field and direction of propagation are mutually perpendicular.
E ⟂ B
and both E and B are perpendicular to the direction of propagation.
2. No material medium is required
Electromagnetic waves can travel through vacuum.
3. They travel with the speed of light in vacuum
c = 3 × 10⁸ m/s
4. They carry energy
Electromagnetic waves transport energy from one place to another.
5. They carry momentum
Electromagnetic radiation can transfer momentum and can therefore exert radiation pressure.
6. Electric and magnetic fields are in phase
The electric field and magnetic field reach their maximum and minimum values simultaneously.
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6. Speed of Electromagnetic Waves
The speed of electromagnetic waves in vacuum is:
c = 1 / √(μ₀ε₀)
where:
μ₀ = permeability of free space
and
ε₀ = permittivity of free space
The value of speed is approximately:
c = 3 × 10⁸ m/s
In a medium, the speed of an electromagnetic wave is generally less than its speed in vacuum.
The refractive index of a medium is related to the speed by:
n = c/v
where:
– n = refractive index
– c = speed of light in vacuum
– v = speed of light in the medium
Therefore:
v = c/n
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7. Relation Between Electric and Magnetic Fields
A very important formula for numerical problems is the relation between the amplitudes of the electric and magnetic fields.
E₀/B₀ = c
Therefore:
E₀ = cB₀
or
B₀ = E₀/c
where:
– E₀ = amplitude of electric field
– B₀ = amplitude of magnetic field
– c = speed of electromagnetic wave in vacuum
Example
If the amplitude of the magnetic field is:
B₀ = 2 × 10⁻⁶ T
then:
E₀ = cB₀
E₀ = 3 × 10⁸ × 2 × 10⁻⁶
Therefore:
E₀ = 600 N/C
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8. Electromagnetic Wave Equation
An electromagnetic wave travelling along the x-axis can be represented by:
E = E₀ sin(kx − ωt)
Similarly, the magnetic field can be written as:
B = B₀ sin(kx − ωt)
Here:
– E₀ = amplitude of electric field
– B₀ = amplitude of magnetic field
– k = wave number
– ω = angular frequency
– x = position
– t = time
The wave number is:
k = 2π/λ
The angular frequency is:
ω = 2πν
where λ is wavelength and ν is frequency.
The basic wave relation is:
v = νλ
For electromagnetic waves in vacuum:
c = νλ
Therefore:
λ = c/ν
and
ν = c/λ
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9. Energy of Electromagnetic Waves
Electromagnetic waves carry energy. This energy is distributed between the electric and magnetic fields.
Energy density associated with the electric field is:
uᴇ = ½ ε₀E²
Energy density associated with the magnetic field is:
uᴮ = B²/(2μ₀)
For an electromagnetic wave in vacuum:
uᴇ = uᴮ
Therefore, the energy is equally divided between the electric and magnetic fields.
The total energy density is:
u = uᴇ + uᴮ
For an electromagnetic wave:
u = ε₀E²
or
u = B²/μ₀
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10. Energy and Intensity of Electromagnetic Radiation
The energy transported by an electromagnetic wave can be described using the Poynting vector.
The instantaneous Poynting vector is:
S = (1/μ₀)(E × B)
Its direction gives the direction of propagation of the electromagnetic wave.
The magnitude of the Poynting vector represents the intensity of energy flow per unit area.
For an electromagnetic wave:
S = EB/μ₀
The average intensity is related to the square of the electric field amplitude:
Iₐᵥg = ½ ε₀cE₀²
It can also be expressed in terms of magnetic field amplitude:
Iₐᵥg = cB₀²/(2μ₀)
These formulas are useful for numerical questions involving the intensity of electromagnetic radiation.
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11. Electromagnetic Spectrum
The electromagnetic spectrum is the complete range of electromagnetic radiation arranged according to wavelength or frequency.
The order from longest wavelength to shortest wavelength is:
Radio Waves → Microwaves → Infrared → Visible Light → Ultraviolet → X-rays → Gamma Rays
As we move from radio waves towards gamma rays:
– Wavelength decreases
– Frequency increases
– Energy increases
The relation between wavelength and frequency is:
c = νλ
The energy of a photon is:
E = hν
Therefore:
E = hc/λ
Hence, shorter wavelength means higher frequency and greater photon energy.
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12. Radio Waves
Radio waves have the longest wavelengths and lowest frequencies in the electromagnetic spectrum.
They are generally produced by oscillating charges in antennas.
Applications of radio waves:
– Radio broadcasting
– Television broadcasting
– Wireless communication
– Communication systems
– Navigation
Radio waves can travel long distances and are therefore very useful for communication.
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13. Microwaves
Microwaves have shorter wavelengths and higher frequencies than radio waves.
Applications:
– Radar
– Satellite communication
– Mobile communication
– Microwave ovens
– Aircraft navigation
Microwaves are particularly useful in radar because they can be transmitted as narrow beams.
In a microwave oven, microwaves cause polar molecules such as water molecules in food to oscillate, producing heating.
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14. Infrared Radiation
Infrared radiation lies between microwaves and visible light.
It is strongly associated with heat and thermal radiation.
All objects at ordinary temperatures emit infrared radiation.
Applications:
– Remote controls
– Thermal imaging
– Night vision
– Heat therapy
– Infrared photography
– Communication systems
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15. Visible Light
Visible light is the small part of the electromagnetic spectrum that can be detected by the human eye.
Its approximate wavelength range is:
400 nm to 700 nm
The colours of visible light are arranged as:
Violet → Indigo → Blue → Green → Yellow → Orange → Red
If arranged from longest wavelength to shortest wavelength, the order is:
Red → Orange → Yellow → Green → Blue → Indigo → Violet
Therefore:
Red has the longest wavelength
and
Violet has the shortest wavelength
within the visible region.
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16. Ultraviolet Radiation
Ultraviolet radiation has a shorter wavelength and higher frequency than visible violet light.
Applications:
– Sterilisation
– Killing microorganisms
– Medical applications
– Detecting forged documents
– Fluorescence studies
Excessive exposure to ultraviolet radiation can damage skin and eyes.
The ultraviolet radiation from the Sun is partly absorbed by the ozone layer.
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17. X-rays
X-rays have very short wavelengths and high frequencies.
They have considerable penetrating power.
Applications:
– Medical imaging
– Detection of bone fractures
– Dental imaging
– Security scanning
– Industrial inspection
X-rays are also used to study the internal structure of materials.
Because X-rays are highly energetic, excessive exposure can damage living tissues.
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18. Gamma Rays
Gamma rays have the shortest wavelengths and highest frequencies in the electromagnetic spectrum.
They are generally associated with nuclear processes and radioactive decay.
Applications:
– Cancer treatment
– Sterilisation of medical equipment
– Nuclear medicine
– Scientific research
Gamma rays have extremely high energy and penetrating power.
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19. Electromagnetic Spectrum – Quick Revision
Radiation| Wavelength| Frequency| Important Uses
Radio waves| Longest| Lowest| Radio, TV, communication
Microwaves| ↓| ↑| Radar, satellites, ovens
Infrared| ↓| ↑| Heat, remote controls
Visible light| ↓| ↑| Vision, optical instruments
Ultraviolet| ↓| ↑| Sterilisation
X-rays| ↓| ↑| Medical imaging
Gamma rays| Shortest| Highest| Cancer treatment, nuclear applications
Remember:
Wavelength order:
Radio > Microwave > Infrared > Visible > Ultraviolet > X-ray > Gamma
Frequency order:
Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma
Energy order:
Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma
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20. Most Important Formulas of Electromagnetic Waves
Speed of electromagnetic waves in vacuum
c = 1 / √(μ₀ε₀)
Speed in a medium
v = c/n
Wave relation
v = νλ
For vacuum:
c = νλ
Frequency
ν = c/λ
Wavelength
λ = c/ν
Angular frequency
ω = 2πν
Wave number
k = 2π/λ
Electric field
E = E₀ sin(kx − ωt)
Magnetic field
B = B₀ sin(kx − ωt)
Relation between E and B
E₀/B₀ = c
or
E₀ = cB₀
Electric energy density
uᴇ = ½ ε₀E²
Magnetic energy density
uᴮ = B²/(2μ₀)
Total energy density
u = ε₀E² = B²/μ₀
Displacement current
Iᵈ = ε₀ × dΦᴇ/dt
Electric flux
Φᴇ = EA cos θ
Poynting vector
S = (1/μ₀)(E × B)
Average intensity
Iₐᵥg = ½ ε₀cE₀²
or
Iₐᵥg = cB₀²/(2μ₀)
Photon energy
E = hν
or
E = hc/λ
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21. Important CBSE Exam Points
Students preparing for Class 12 CBSE Physics should remember the following points:
1. Electromagnetic waves are transverse waves.
2. They do not require a material medium.
3. They can propagate through vacuum.
4. Electric and magnetic fields are mutually perpendicular.
5. Both fields are perpendicular to the direction of propagation.
6. Electric and magnetic fields are in phase.
7. Electromagnetic waves are produced by accelerating charges.
8. The speed of electromagnetic waves in vacuum is 3 × 10⁸ m/s.
9. Light is an electromagnetic wave.
10. Displacement current is associated with a changing electric field.
11. In vacuum, E₀/B₀ = c.
12. All electromagnetic waves have the same speed in vacuum.
13. Frequency and wavelength are inversely related in vacuum.
14. Photon energy is directly proportional to frequency.
15. Gamma rays have the highest frequency and photon energy.
16. Radio waves have the longest wavelength and lowest frequency.
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Conclusion
Electromagnetic Waves is a short but highly scoring chapter in Class 12 Physics. The chapter becomes easy once the relationship between electric fields, magnetic fields, wavelength, frequency and energy is clearly understood.
The most important things to master are Maxwell’s displacement current, the transverse nature of electromagnetic waves, their speed in vacuum, the relation E₀ = cB₀, energy density, Poynting vector, photon energy and the electromagnetic spectrum.
Students should especially memorise the spectrum in the correct order:
Radio → Microwave → Infrared → Visible → Ultraviolet → X-rays → Gamma
and remember that from radio waves towards gamma rays, wavelength decreases while frequency and photon energy increase.
A strong command of the formulas and applications discussed in this chapter can help students answer conceptual questions, MCQs, assertion-reason questions and numerical problems quickly and accurately.
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