Laser Physics I - Lecture One

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Questions and Answers

What describes the nature of electromagnetic waves?

  • They involve simultaneous variations of electric and magnetic fields. (correct)
  • They have a constant speed that varies with amplitude.
  • They are produced by static electric and magnetic fields.
  • They travel in longitudinal waves.

Which property of electromagnetic waves is influenced by the medium they travel in?

  • The amplitude of the electric field.
  • The direction of propagation.
  • The speed of the waves. (correct)
  • The frequency of the waves.

Which mathematical framework is fundamental for understanding electromagnetics?

  • Newton's laws of motion.
  • Quantum mechanics.
  • Thermodynamics.
  • Maxwell's equations. (correct)

What does Gauss' law for electricity mathematically express?

<p>The divergence of electric displacement equals charge density. (B)</p> Signup and view all the answers

What aspect do all electromagnetic waves share?

<p>Their speeds are constant in a vacuum. (A)</p> Signup and view all the answers

What does Faraday’s law of induction indicate?

<p>A changing magnetic field induces an electric field. (A)</p> Signup and view all the answers

What does the term 'transverse wave' refer to in the context of electromagnetic waves?

<p>Waves that move perpendicular to the direction of energy transfer. (C)</p> Signup and view all the answers

Which equation represents Ampere’s law?

<p>$ abla imes ext{H} = ext{J} + rac{ ext{dD}}{ ext{dt}}$ (A)</p> Signup and view all the answers

What does Gauss' law for electricity indicate about positive charge?

<p>It acts as a source for electric fields. (A)</p> Signup and view all the answers

What does Gauss' law for magnetism state about magnetic monopoles?

<p>Every magnet behaves as a dipole with distinct poles. (D)</p> Signup and view all the answers

Which statement correctly describes Faraday's law of induction?

<p>A time-varying magnetic flux generates an electric field. (B)</p> Signup and view all the answers

According to Ampere's law, what can create a magnetic field?

<p>Either a current density or a displacement current. (D)</p> Signup and view all the answers

How are electric flux density D and electric field E related in free space?

<p>D = ε₀ E (B)</p> Signup and view all the answers

What is the divergence of the magnetic field B according to Gauss' law for magnetism?

<p>It is zero. (C)</p> Signup and view all the answers

What does the permittivity of free space ε₀ denote?

<p>The constant that relates electric flux density and electric field. (D)</p> Signup and view all the answers

In free space, which equation relates magnetic flux density B and magnetic field strength H?

<p>B = μ₀ H (C)</p> Signup and view all the answers

What operation is applied to both sides of the third equation of Maxwell’s equations to derive the wave equation?

<p>Curl (A)</p> Signup and view all the answers

Which equation represents Faraday's law in Maxwell's equations?

<p>∇ × E = -∂B/∂t (A)</p> Signup and view all the answers

In free space, what is the value of the current density J when substituted into Maxwell's fourth equation?

<p>0 (B)</p> Signup and view all the answers

What does the equation D = ε₀E represent?

<p>Electric displacement field (B)</p> Signup and view all the answers

Substituting the equation D = ε₀E in the wave equation results in which of the following?

<p>∇²E = μ₀ε₀∂²E/∂t² (A)</p> Signup and view all the answers

What is the relationship between the speed of light c, permeability μ₀, and permittivity ε₀?

<p>c = 1/(μ₀ε₀) (B)</p> Signup and view all the answers

Which of the following represents the complete wave equation derived from Maxwell's equations?

<p>∇²E - 1/(c²)∂²E/∂t² = 0 (A)</p> Signup and view all the answers

What does the term ∇²E in the context of electromagnetic waves refer to?

<p>The Laplacian of the electric field (B)</p> Signup and view all the answers

What direction do both electric and magnetic fields travel in electromagnetic waves?

<p>Z direction (B)</p> Signup and view all the answers

Which quantity represents the angular frequency in the sinusoidal solution of the electromagnetic wave?

<p>ω (B)</p> Signup and view all the answers

In the wave equation for the electric field, which term represents the speed of the wave?

<p>c (B)</p> Signup and view all the answers

What is the relationship between electric field (E) and magnetic field (B) in electromagnetic waves as given by Maxwell's equations?

<p>E = cB (C)</p> Signup and view all the answers

Which equation represents the wave equation derived for the electric field?

<p>$ \frac{\partial^2 E_x}{\partial z^2} = \frac{1}{c^2} \frac{\partial^2 E_x}{\partial t^2} $ (A)</p> Signup and view all the answers

In the sinusoidal representation of electromagnetic waves, what does the term $E_0$ represent?

<p>Amplitude (D)</p> Signup and view all the answers

What is the wavenumber (k) in the context of electromagnetic waves?

<p>Number of wavelengths per unit distance (D)</p> Signup and view all the answers

According to Maxwell's equations, what equation describes the relationship between the time derivative of magnetic field and the electric field?

<p>$ \nabla \times E = - \frac{\partial B}{\partial t} $ (B)</p> Signup and view all the answers

Flashcards

What are Electromagnetic Waves (EMW)?

Electromagnetic waves (EMW) are disturbances that propagate through space by the interaction of electric and magnetic fields.

What are the properties of Electromagnetic Waves?

Changes in electric and magnetic fields occur simultaneously. They reach their maximum and minimum points at the same time and location. The electric and magnetic fields are perpendicular to each other and the direction of wave propagation.

What determines the speed of EMW?

The speed of Electromagnetic Waves depends only on the properties of the medium they travel through. It's not affected by the strength of the electric or magnetic fields.

What are Maxwell's Equations?

Maxwell's equations are a set of mathematical equations that describe how electric and magnetic fields behave. They explain how these fields travel through space and interact with each other.

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Describe Maxwell's Equations.

A set of four equations that relate electric and magnetic fields. These equations are fundamental to understanding how electromagnetic waves behave and interact.

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What is Gauss' Law for Electricity?

The total electric flux out of a closed surface is proportional to the total electric charge enclosed by the surface.

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What is Gauss' Law for Magnetism?

The total magnetic flux leaving a closed surface is always zero. This implies that there is no magnetic monopole, only dipoles.

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What is Faraday's Law of Induction?

The line integral of the electric field around a closed loop is equal to the negative rate of change of the magnetic flux through the loop.

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Gauss's Law for Electricity

The divergence of electric flux density (D) is equal to the volume electric charge density. Positive charges act as sources, creating outward electric flux, while negative charges act as sinks, causing inward electric flux.

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Gauss's Law for Magnetism

The divergence of magnetic flux density (B) is zero. Magnetic monopoles (isolated north or south poles) don't exist, and magnetic fields always form closed loops.

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Faraday's Law of Induction

A time-varying magnetic flux induces an electric field. The principle behind electric generators where moving magnetic fields induce current in wires.

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Ampere's Law

Both current density (moving charges) and a time-varying displacement current (changing electric field) create magnetic fields. This is why sending current through a wire generates a magnetic field around it.

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Electric Flux Density in Free Space

The relationship between electric flux density (D) and electric field (E) in free space. It's determined by the permittivity of free space (ε₀).

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Magnetic Flux Density in Free Space

The relationship between magnetic flux density (B) and magnetic field (H) in free space. It's determined by the permeability of free space (μ₀).

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Permittivity (ε)

The ability of a material to store electric energy in an electric field. The higher permittivity, the more charge a material can store.

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Permeability (μ)

The ability of a material to store magnetic energy in a magnetic field. The higher permeability, the more magnetic field can be stored in the material.

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Curl Operation

A mathematical operation that determines the rate of change of a vector field with respect to position.

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Faraday's Law

Maxwell's first equation relating the curl of the electric field (E) to the rate of change of the magnetic field (B) with respect to time.

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Wave Equation for Electric Field

The equation that describes how electromagnetic waves propagate through space. It relates the second derivative of the electric field (E) with respect to time to the second derivative of the electric field with respect to position.

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Electric Field (E)

A vector quantity that describes the density and direction of the electric field.

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Magnetic Field (B)

A vector quantity that describes the density and direction of the magnetic field.

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Magnetic Field Intensity (H)

A vector quantity that describes the density and direction of the magnetic field intensity.

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Electric Displacement Field (D)

A vector quantity that describes the density and direction of the electric displacement field.

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Wave Equation for Magnetic Field

A mathematical equation describing how electric and magnetic fields propagate as waves.

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Sinusoidal EMW (Electric field)

The simplest solution to the wave equation, representing the electric field as a sinusoidal wave.

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Sinusoidal EMW (Magnetic field)

The simplest solution to the wave equation, representing the magnetic field as a sinusoidal wave.

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Equation: E = cB

This equation relates the electric field strength (E) to the magnetic field strength (B), the speed of light (c), and the wave number (k) and angular frequency (w) of the electromagnetic wave. It shows the essential relationship between E and B in an electromagnetic wave.

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Faraday's Law (3rd Maxwell's Equation)

The rate at which the electric field changes over time is equal to the negative rate of change of the magnetic field.

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Maxwell's Equations

A collection of equations that describe the fundamental principles of electromagnetism and how they interact with each other and with matter.

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Electromagnetic Waves (EMW)

Disturbances that propagate through space and carry energy. These disturbances are made up of oscillating electric and magnetic fields that are perpendicular to each other and to the direction the wave is traveling.

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Study Notes

Laser Physics I - Lecture One

  • The lecturer is Dr. Fatema H. Rajab
  • Department: Laser and Optoelectronics Engineering
  • University: Al-Nahrain University, Baghdad, IRAQ
  • Email addresses and mobile number are provided for contact

Electromagnetic Waves

  • Electromagnetic waves (EMW) are generated by vibrations between electric and magnetic fields.
  • EMW are transverse waves, meaning the electric and magnetic fields are perpendicular to each other and the direction of wave propagation.
  • The strength (amplitude) of the EMW does not affect the wave speed, which depends only on the medium's electric and magnetic properties.
  • The electric and magnetic fields change simultaneously reaching maximum and minimum values at the same time and place.

Maxwell's Equations

  • Maxwell's equations describe the interactions and propagation of electromagnetic fields, and how they are influenced by objects.

  • They are a set of partial differential equations.

  • Maxwell's equations form the basis for understanding and mathematically characterizing many aspects of EM wave theory.

  • The equations are

    • Gauss's law for electricity: ∇⋅D = ρ
    • Gauss's law for magnetism: ∇⋅B = 0
    • Faraday's law of induction: ∇ × E = -dB/dt
    • Ampere's law: ∇ × H = J + dD/dt

  • The variables are defined as:

    • D: electric flux density or electric displacement
    • B: magnetic flux density or magnetic induction
    • E: electric field intensity
    • H: magnetic field intensity
    • ρ: volume charge density
    • J: electric current density

  • In free space:

    • D = ε₀E
    • B = μ₀H

  • Values for ε₀ (permittivity of free space) and μ₀ (permeability of free space) are provided.

  • Starting from Faraday's law (∇ × E = -dB/dt), the wave equation for the electric field can be derived. This involves applying the curl operation and using other Maxwell's equations.

  • The derived wave equation is: (\nabla^2 E = -\mu_0\epsilon_0\frac{\partial^2E}{\partial t^2}).

    • This equation shows how changes in the electric field propagate as waves.

Electromagnetic Wave Equation

  • Electromagnetic waves travel in the z-direction.
  • Electric field amplitude is in the x-axis
  • Magnetic field amplitude is in the y-axis.
  • The general expression is given by
    • E = Ex(z, t) = E₀ cos(kz - ωt)x
    • B = By(z,t) = B₀ cos(kz - ωt)y
  • The simplest solution is a sinusoidal electromagnetic wave, where ω represents angular frequency, and k represents the wavenumber.
  • The speed of light (c) in a vacuum is related to the permeability and permittivity of free space as follows: ( c = 1/\sqrt{\mu_0\epsilon_0} ).

Possible Questions (from the presentation)

  • State Maxwell's equations with a brief description.
  • List main properties of electromagnetic waves.
  • Starting from Maxwell's equations, derive the wave equation for the electric field.
  • Starting from Maxwell's equations, derive the wave equation for the electric field with its solution.
  • Multiple choice questions of point (1, 2).
  • If the electric field of a wave is 7 V/m, find the magnetic field flux density (magnetic field B).

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