Slide 1
- Topic: Problems In Electromagnetics- Magnetic Fields, EM Waves
- Introduction to the topic
Slide 2
- Magnetic field properties
- Definition: Magnetic field
- Magnetic field lines
- Magnetic field strength (B)
- Magnetic flux (Φ)
Slide 3
- Magnetic field due to a straight current-carrying conductor
- Right-hand thumb rule
- Magnetic field formula: B = (μ₀I) / (2πr)
- Magnetic field inside a solenoid
Slide 4
- Magnetic field due to a circular current-carrying loop
- Magnetic field at the center of the loop
- Magnetic field along the axis of the loop
- Magnetic field formula: B = (μ₀I) / (2R)
Slide 5
- Electromagnetic waves (EM waves)
- Definition of EM waves
- Properties of EM waves
- Electromagnetic spectrum
Slide 6
- The electric field of a plane EMW propagating in free space
- Equation: E = E₀ sin(kz - ωt)
- Explanation of the variables in the equation
Slide 7
- Wave propagation and wavefronts
- Wavefronts and rays
- Spherical wavefronts
- Plane wavefronts
Slide 8
- Speed of light and refractive index
- Definition of the speed of light (c)
- Relation between speed of light and refractive index (v = c / n)
- Refractive index of different mediums
Slide 9
- Reflection and refraction of EM waves
- Laws of reflection
- Laws of refraction (Snell’s law)
- Refractive index and angles of incidence and refraction
Slide 10
- Total internal reflection
- Conditions for total internal reflection
- Critical angle
- Applications of total internal reflection
- The electric field of a plane EMW propagating in free space
- Equation: E = E₀ sin(kz - ωt)
- Explanation of the variables in the equation
- E₀: Amplitude of the electric field
- k: Wave number (k = 2π / λ, where λ is the wavelength)
- z: Distance along the direction of propagation
- ω: Angular frequency (ω = 2πf, where f is the frequency)
- t: Time
- Wave propagation and wavefronts
- Wavefronts and rays
- Wavefront: A surface that connects all the points of a wave that are in the same phase
- Ray: A line perpendicular to the wavefronts, indicating the direction of wave propagation
- Spherical wavefronts
- Wavefronts that spread out in all directions from a point source
- Plane wavefronts
- Wavefronts that are flat and parallel to each other, indicating a plane wave
- Speed of light and refractive index
- Definition of the speed of light (c)
- Speed of light in a vacuum: 2.998 x 10^8 m/s
- Relation between speed of light and refractive index (v = c / n)
- Refractive index (n): Ratio of the speed of light in a vacuum to the speed of light in a medium
- Refractive index of different mediums
- Examples: Air (n ≈ 1), Water (n ≈ 1.333), Glass (n ≈ 1.5-1.7)
- Reflection and refraction of EM waves
- Laws of reflection
- Incident angle = Reflected angle (θi = θr)
- Incident ray, reflected ray, and normal line lie in the same plane
- Laws of refraction (Snell’s law)
- n₁sinθ₁ = n₂sinθ₂ (n₁, n₂: Refractive indices; θ₁, θ₂: Incident and refracted angles)
- Refractive index and angles of incidence and refraction
- Total internal reflection
- Conditions for total internal reflection
- Incident angle > Critical angle
- Critical angle
- The angle of incidence that results in an angle of refraction of 90 degrees
- Defined by n₁sinθc = n₂, where θc is the critical angle
- Applications of total internal reflection
- Electromagnetic induction
- Introduction to electromagnetic induction
- Faraday’s law of electromagnetic induction
- Induced emf = -N dΦ / dt (N: Number of turns, Φ: Magnetic flux)
- Lenz’s law
- The direction of the induced current or emf opposes the change producing it
- Magnetic flux and electromagnetic induction
- Definition of magnetic flux (Φ)
- Φ = B A cosθ (B: Magnetic field, A: Area, θ: Angle between B and A)
- Magnetic flux through a coil
- Φ = B A cosθ = B A (θ = 0° for maximum flux)
- Magnetic flux-linkage
- Φ = B A cosθ (Φ = B A N for N turns)
- Faraday’s law of electromagnetic induction
- Induced emf (ε) in a coil
- ε = -dΦ / dt (ε: Induced emf, Φ: Magnetic flux)
- Direction of induced current
- Depends on the direction of change in magnetic flux and the direction of the coil
- Lenz’s law and conservation of energy
- Lenz’s law
- The direction of the induced current or emf opposes the change producing it
- Induced current creates a magnetic field that opposes the change in the external magnetic field
- Conservation of energy
- Energy is conserved in the process of electromagnetic induction
- Self-induction and inductance
- Self-induction
- The phenomenon of producing an induced emf in a coil due to changes in its own current
- Inductance (L)
- A property of a circuit that determines the self-induced emf
- Defined as the ratio of the induced emf to the rate of change of current (L = ε / di / dt)
Slide 21
- The electric field of a plane EMW propagating in free space is given by the equation: E = E₀ sin(kz - ωt)
- Explanation of the variables in the equation:
- E₀: Amplitude of the electric field
- k: Wave number (k = 2π / λ, where λ is the wavelength)
- z: Distance along the direction of propagation
- ω: Angular frequency (ω = 2πf, where f is the frequency)
- t: Time
Slide 22
- Wave propagation and wavefronts:
- Wavefronts and rays:
- Wavefront: A surface that connects all the points of a wave that are in the same phase
- Ray: A line perpendicular to the wavefronts, indicating the direction of wave propagation
- Spherical wavefronts:
- Wavefronts that spread out in all directions from a point source
- Plane wavefronts:
- Wavefronts that are flat and parallel to each other, indicating a plane wave
Slide 23
- Speed of light and refractive index:
- Definition of the speed of light (c):
- Speed of light in a vacuum: 2.998 x 10^8 m/s
- Relation between speed of light and refractive index (v = c / n):
- Refractive index (n): Ratio of the speed of light in a vacuum to the speed of light in a medium
- Refractive index of different mediums:
- Examples: Air (n ≈ 1), Water (n ≈ 1.333), Glass (n ≈ 1.5-1.7)
Slide 24
- Reflection and refraction of EM waves:
- Laws of reflection:
- Incident angle = Reflected angle (θi = θr)
- Incident ray, reflected ray, and normal line lie in the same plane
- Laws of refraction (Snell’s law):
- n₁sinθ₁ = n₂sinθ₂ (n₁, n₂: Refractive indices; θ₁, θ₂: Incident and refracted angles)
- Refractive index and angles of incidence and refraction
Slide 25
- Total internal reflection:
- Conditions for total internal reflection:
- Incident angle > Critical angle
- Critical angle:
- The angle of incidence that results in an angle of refraction of 90 degrees
- Defined by n₁sinθc = n₂, where θc is the critical angle
- Applications of total internal reflection
Slide 26
- Electromagnetic induction:
- Introduction to electromagnetic induction
- Faraday’s law of electromagnetic induction:
- Induced emf = -N dΦ / dt (N: Number of turns, Φ: Magnetic flux)
- Lenz’s law:
- The direction of the induced current or emf opposes the change producing it
Slide 27
- Magnetic flux and electromagnetic induction:
- Definition of magnetic flux (Φ):
- Φ = B A cosθ (B: Magnetic field, A: Area, θ: Angle between B and A)
- Magnetic flux through a coil:
- Φ = B A cosθ = B A (θ = 0° for maximum flux)
- Magnetic flux-linkage:
- Φ = B A cosθ (Φ = B A N for N turns)
Slide 28
- Faraday’s law of electromagnetic induction:
- Induced emf (ε) in a coil:
- ε = -dΦ / dt (ε: Induced emf, Φ: Magnetic flux)
- Direction of induced current:
- Depends on the direction of change in magnetic flux and the direction of the coil
Slide 29
- Lenz’s law and conservation of energy:
- Lenz’s law:
- The direction of the induced current or emf opposes the change producing it
- Induced current creates a magnetic field that opposes the change in the external magnetic field
- Conservation of energy:
- Energy is conserved in the process of electromagnetic induction
Slide 30
- Self-induction and inductance:
- Self-induction:
- The phenomenon of producing an induced emf in a coil due to changes in its own current
- Inductance (L):
- A property of a circuit that determines the self-induced emf
- Defined as the ratio of the induced emf to the rate of change of current (L = ε / di / dt)