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Questions and Answers
What limitation does Ampere's law have when current changes over time?
What limitation does Ampere's law have when current changes over time?
What is produced by a changing electric field?
What is produced by a changing electric field?
In an RC circuit, what happens to the current over time?
In an RC circuit, what happens to the current over time?
How is the displacement current related to the electric field between capacitor plates?
How is the displacement current related to the electric field between capacitor plates?
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What is the relationship between voltage and electric field in a capacitor?
What is the relationship between voltage and electric field in a capacitor?
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In the context of Maxwell's equations, what does Gauss's law state about electric flux?
In the context of Maxwell's equations, what does Gauss's law state about electric flux?
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What phenomenon occurs between capacitor plates that can't be crossed by charge movement?
What phenomenon occurs between capacitor plates that can't be crossed by charge movement?
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When measuring electric flux through a closed surface, what must be accounted for according to Gauss's law?
When measuring electric flux through a closed surface, what must be accounted for according to Gauss's law?
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What is the relationship between wavelength, frequency, and the speed of light in a vacuum?
What is the relationship between wavelength, frequency, and the speed of light in a vacuum?
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What is the unit of frequency and how is it defined?
What is the unit of frequency and how is it defined?
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Which color of visible light has the longest wavelength?
Which color of visible light has the longest wavelength?
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What does the Poynting vector describe?
What does the Poynting vector describe?
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How is the relationship between power and intensity mathematically expressed?
How is the relationship between power and intensity mathematically expressed?
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What does the angular frequency relate to in wave motion?
What does the angular frequency relate to in wave motion?
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Which of the following is true about radiation pressure?
Which of the following is true about radiation pressure?
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What is the approximate wavelength range of visible light?
What is the approximate wavelength range of visible light?
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What does Gauss's law for magnetism state about magnetic field lines?
What does Gauss's law for magnetism state about magnetic field lines?
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In an electromagnetic wave, how are the electric field (E) and magnetic field (B) oriented with respect to each other?
In an electromagnetic wave, how are the electric field (E) and magnetic field (B) oriented with respect to each other?
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What is the source of any electromagnetic wave?
What is the source of any electromagnetic wave?
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According to the wave equation, if an electromagnetic wave is propagating in the x direction, in which direction does the E field oscillate?
According to the wave equation, if an electromagnetic wave is propagating in the x direction, in which direction does the E field oscillate?
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How is the speed of light in a vacuum denoted and what is its approximate value?
How is the speed of light in a vacuum denoted and what is its approximate value?
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What effect does a changing magnetic field have on the electric field according to Faraday's law?
What effect does a changing magnetic field have on the electric field according to Faraday's law?
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What is Ampere-Maxwell law primarily concerned with?
What is Ampere-Maxwell law primarily concerned with?
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How do the magnitudes of the electric and magnetic fields relate in a vacuum?
How do the magnitudes of the electric and magnetic fields relate in a vacuum?
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Study Notes
Electromagnetic (EM) Waves
- Electromagnetic waves are produced by changing electric fields.
- Ampère's law is insufficient when current changes over time (e.g., in an RC circuit).
- A changing electric field creates a magnetic field, and vice versa.
- Displacement current (Id) accounts for changes in electric flux over time, analogous to a current.
- Id is related to the rate of change of electric flux.
- Id = ε₀ * (dΦE/dt)
- Maxwell's equations describe the relationship between electric and magnetic fields.
Maxwell's Equations
- Gauss's Law (electric): Electric flux through a closed surface is proportional to the enclosed charge. (ΦE = Qenc/ε₀)
- Gauss's Law (magnetism): Magnetic flux through a closed surface is zero. (ΦB = 0)
- Faraday's Law: A changing magnetic field induces an electric field. (∮E•dl = -dΦB/dt)
- Ampère-Maxwell Law: A changing electric field or a conduction current produces a magnetic field. (∮B•dl = μ₀Ienc + μ₀ε₀dΦE/dt)
Electromagnetic Waves Properties
- Light is a transverse electromagnetic wave.
- Electromagnetic waves travel at the speed of light (c) in a vacuum.
- In a vacuum c = 1/√(μ₀ε₀)
- The electric and magnetic fields are perpendicular to each other and the direction of propagation.
- Electric and magnetic fields oscillate sinusoidally.
- Electromagnetic waves are characterized by their wavelength (λ) and frequency (f).
- c = λf
Wave Vector
- The wave vector (k) is related to wavelength and frequency
- k = 2π/λ
Poynting Vector
- The Poynting vector (S) describes the flow of electromagnetic energy. (S = E × B / μ₀)
- S has a magnitude and direction.
- Intensity (I) is the time-averaged magnitude of S.
- I = Savg = (1/2μ₀)|E|² = (1/2μ₀)|B|²
- Radiation Pressure: Force per unit area exerted by an EM wave
- Prad = I/c if object is an absorber
- Prad = 2 I/c if object is a perfect reflector
Wavelength and Color
- Visible light has wavelengths ranging from approximately 400 nm (violet) to 700 nm (red).
- Different wavelengths correspond to different colors and energies.
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Description
Explore the fundamental principles behind electromagnetic waves and Maxwell's equations in this quiz. Learn how changing electric fields relate to magnetic fields, and test your understanding of Gauss's laws, Faraday's law, and the Ampère-Maxwell law. Perfect for students studying physics or electromagnetic theory.
