Slide 1

• Displacement current: an important concept in electromagnetism.
• It plays a crucial role in the generation of electromagnetic waves.
• Displacement current is a concept introduced by James Clerk Maxwell.
• It explains the relationship between changing electric fields and magnetic fields.
• It is important to understand the displacement current to comprehend the generation of electromagnetic waves.

Slide 2

• Maxwell’s equations: a set of fundamental equations in electromagnetism.
• These equations describe how electric and magnetic fields are related to charges and currents.
• Displacement current is incorporated into Maxwell’s equations.
• The equations consist of four laws: Gauss’s law, Gauss’s law for magnetism, Faraday’s law of induction, and Ampere’s law with Maxwell’s addition.

Slide 3

• Ampere’s law: originally formulated by André-Marie Ampère.
• Ampere’s law relates the magnetic field circulating around a closed loop to the electric current passing through the loop.
• Ampere’s law states that the circulation of the magnetic field is proportional to the electric current passing through the loop.
• Maxwell’s addition to Ampere’s law introduces the concept of displacement current.

Slide 4

• Displacement current in Ampere’s law: Maxwell’s addition.
• Displacement current is a term added to Ampere’s law to account for the changing electric fields.
• The displacement current is denoted as ‘Id’.
• It is expressed as:
  • Id = ε₀ * dΦe/dt
  • Where ε₀ represents the permittivity of free space and dΦe/dt represents the rate of change of electric flux.

Slide 5

• Electric flux: the measure of the electric field passing through a surface.
• Electric flux is given by the equation:
  • Φe = ∫E ⋅ dA
  • Where E represents the electric field and dA represents an infinitesimal area element.
• The displacement current depends on the rate of change of electric flux.

Slide 6

• Relationship between displacement current and changing electric fields.
• When the electric field through a surface changes, a displacement current is produced.
• The displacement current flows in a direction that complements the changing electric field.
• A changing electric field induces a magnetic field, and vice versa.
• The displacement current contributes to the changing magnetic field.

Slide 7

• Electromagnetic wave generation: the role of displacement current.
• The generation of electromagnetic waves involves the interplay of changing electric and magnetic fields.
• Displacement current is responsible for the changing magnetic field that is essential for the propagation of electromagnetic waves.
• Without the displacement current, electromagnetic waves cannot be generated.

Slide 8

• Example: Charging a capacitor.
• When a capacitor is connected to a battery, it charges up.
• Throughout the charging process, there is a change in electric field.
• The changing electric field creates a displacement current.
• This displacement current is necessary for the charging process to occur.

Slide 9

• Example: Radio waves.
• Radio waves are a form of electromagnetic waves.
• These waves are generated by rapidly changing electric fields.
• The changing electric fields result in a displacement current.
• The displacement current contributes to the generation of radio waves.

Slide 10

• Summary:
  • Displacement current is a concept introduced by Maxwell in his equations.
  • It accounts for the changing electric fields and contributes to the generation of electromagnetic waves.
  • Displacement current is incorporated into Ampere’s law to explain the relationship between changing electric fields and magnetic fields.
  • Examples of the importance of displacement current include charging a capacitor and the generation of radio waves.

Slide 11

• Electromagnetic waves: transverse waves that consist of oscillating electric and magnetic fields.
• They do not require a medium to propagate and can travel through vacuum.
• Electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
• The spectrum of electromagnetic waves is organized based on their wavelengths and frequencies.
• Electromagnetic waves have various applications in communication, energy transfer, imaging, and more.

Slide 12

• Electromagnetic spectrum: a range of all possible electromagnetic waves.
• It is organized based on increasing wavelengths and decreasing frequencies.
• The spectrum is divided into several regions:
  • Radio waves: longest wavelength and lowest frequency.
  • Microwaves: slightly shorter wavelength and higher frequency.
  • Infrared: shorter wavelength and higher frequency.
  • Visible light: a narrow range of wavelengths that are visible to the human eye.
  • Ultraviolet: shorter wavelength and higher frequency than visible light.
  • X-rays: shorter wavelength and higher frequency than ultraviolet.
  • Gamma rays: shortest wavelength and highest frequency.

Slide 13

• Electromagnetic wave properties:
  1. They travel at the speed of light, which is approximately 3 x 10^8 m/s in a vacuum.
  2. They can be reflected, refracted, and diffracted like other types of waves.
  3. The energy of electromagnetic waves is directly proportional to their frequency.
  4. They follow the principles of superposition, interference, and polarization.
  5. Electromagnetic waves are emitted and absorbed by charged particles.

Slide 14

• Electromagnetic wave equations:
  • The speed of light (c) is related to the frequency (f) and wavelength (λ) of an electromagnetic wave by the equation: c = fλ.
  • The energy (E) of an electromagnetic wave is related to its frequency by the equation: E = hf, where h is Planck’s constant.
  • The wave number (k) of an electromagnetic wave is related to its wavelength by the equation: k = 2π/λ.

Slide 15

• The relationship between wavelength and frequency:
  • As the wavelength increases, the frequency decreases, and vice versa.
  • This relationship holds true for all types of electromagnetic waves.
  • The energy of an electromagnetic wave is directly proportional to its frequency, so shorter wavelengths correspond to higher energy waves.

Slide 16

• Propagation of electromagnetic waves:
  • Electromagnetic waves propagate in a direction perpendicular to both the electric and magnetic fields.
  • The electric and magnetic fields are in-phase and perpendicular to each other.
  • As the wave propagates, the electric and magnetic fields oscillate in a synchronized manner.
  • The amplitude of the electric and magnetic fields decreases as the wave travels away from its source.

Slide 17

• Electromagnetic wave polarization:
  • Polarization refers to the orientation of the electric field vector of an electromagnetic wave.
  • Electromagnetic waves can be polarized in different ways:
    1. Linear polarization: the electric field oscillates in a single plane.
    2. Circular polarization: the electric field rotates in a circle as the wave propagates.
    3. Elliptical polarization: the electric field traces out an elliptical pattern.

Slide 18

• Applications of electromagnetic waves:
  • Radio waves: used in communication, broadcasting, and radar systems.
  • Microwaves: used in cooking, communication (satellite and wireless), and radar.
  • Infrared: used in remote controls, thermal imaging, and communication.
  • Visible light: used in vision, optical communications, and photography.
  • Ultraviolet: used in sterilization, fluorescence, and security identification.
  • X-rays: used in medical imaging and security screening.
  • Gamma rays: used in cancer treatment, sterilization, and radiation therapy.

Slide 19

• Electromagnetic wave detection:
  • Different types of electromagnetic waves are detected using specific devices:
    1. Radio waves: antennas and receivers (radio receivers, televisions, etc.).
    2. Microwaves: waveguides (microwave ovens, satellite communication).
    3. Infrared: sensors and detectors (night vision devices, remote controls).
    4. Visible light: eyes and cameras.
    5. Ultraviolet: UV detectors and fluorescent materials.
    6. X-rays and gamma rays: photographic film, scintillation detectors, and image detectors.

Slide 20

• Summary:
  • Electromagnetic waves are transverse waves consisting of oscillating electric and magnetic fields.
  • They have various wavelengths and frequencies, organized in the electromagnetic spectrum.
  • Electromagnetic waves travel at the speed of light, follow wave equations and exhibit properties like reflection and interference.
  • The polarization and energy of electromagnetic waves also play significant roles.
  • Electromagnetic waves have numerous applications and can be detected using specific devices.

Slide 21

• Electromagnetic wave interactions:
  • Reflection: when an electromagnetic wave strikes a surface and bounces back.
  • Refraction: when an electromagnetic wave passes through a boundary between two different media and changes direction.
  • Diffraction: when an electromagnetic wave bends around an obstacle or passes through a narrow opening.
  • Interference: when two or more waves meet, resulting in constructive or destructive interference.
  • Absorption: when an electromagnetic wave is absorbed by a material, transferring its energy to the material.

Slide 22

• Reflection of electromagnetic waves:
  • Angle of incidence: the angle between the incident wave and the normal to the reflecting surface.
  • Angle of reflection: the angle between the reflected wave and the normal to the reflecting surface.
  • Law of reflection: the angle of incidence is equal to the angle of reflection.
  • Specular reflection: reflection from a smooth surface, where the incident and reflected waves are parallel.
  • Diffuse reflection: reflection from a rough surface, where the incident and reflected waves are scattered in various directions.

Slide 23

• Refraction of electromagnetic waves:
  • Refraction occurs when an electromagnetic wave passes from one medium to another with a different refractive index.
  • The refractive index (n) of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium.
  • Snell’s Law: it describes the relationship between the angles of incidence and refraction.
  • Snell’s Law: n1 sin(θ1) = n2 sin(θ2)
  • Where n1 and n2 are the refractive indices of the initial and final media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

Slide 24

• Total internal reflection:
  • Total internal reflection occurs when an electromagnetic wave passes from a medium with a higher refractive index to a medium with a lower refractive index.
  • It happens at an angle of incidence greater than the critical angle, where the refracted wave is entirely reflected back into the medium of higher refractive index.
  • The critical angle can be calculated using: θc = sin^(-1)(n2/n1)
  • Total internal reflection is important in technologies like fiber optics and prism-based devices.

Slide 25

• Diffraction of electromagnetic waves:
  • Diffraction occurs when an electromagnetic wave encounters an obstacle or passes through a narrow opening.
  • The amount of diffraction depends on the wavelength of the wave and the size of the obstacle or opening.
  • Diffraction can cause waves to bend around corners or spread out after passing through an opening.
  • The phenomenon of diffraction is observed in various natural and man-made scenarios, including sound waves, light waves, and water waves.

Slide 26

• Interference of electromagnetic waves:
  • Interference occurs when two or more waves overlap or meet.
  • Constructive interference: occurs when the crests of two waves coincide, resulting in a wave with increased amplitude.
  • Destructive interference: occurs when the crest of one wave coincides with the trough of another wave, resulting in a wave with decreased amplitude.
  • Interference patterns can be observed in experiments with double-slit setups or thin films.

Slide 27

• Absorption of electromagnetic waves:
  • Absorption refers to the process in which an electromagnetic wave’s energy is absorbed by a material or medium it encounters.
  • The absorbed energy is converted into other forms, such as heat.
  • Different materials have varying abilities to absorb electromagnetic waves.
  • Absorption is utilized in various applications, including solar panels, microwave ovens, and light-absorbing pigments.

Slide 28

• Example: Reflection of light from a mirror:
  • When a light wave strikes a mirror, it undergoes reflection.
  • The angle of incidence is equal to the angle of reflection.
  • The normal is a line perpendicular to the surface of the mirror.
  • The reflected wave bounces back and forms an image in the mirror.
  • This phenomenon is utilized in mirrors, telescopes, and other reflective devices.

Slide 29

• Example: Refraction of light in different media:
  • Light waves undergo refraction when they pass from one medium to another with a different refractive index.
  • The refractive index determines the speed of light in a medium.
  • Refraction causes light waves to change direction, and this effect can be observed when a straw appears bent in a glass of water.
  • Lenses and prisms utilize the bending of light through refraction.

Slide 30

• Example: Diffraction of sound waves:
  • Sound waves can diffract around obstacles or through openings.
  • For example, when sound waves encounter a door, they bend around the edges and continue to propagate into another room.
  • The phenomenon of diffraction allows us to hear sound even when the direct path is obstructed.
  • Diffraction is also utilized in designing concert halls and soundproofing rooms.