Who showed that a time-varying electric field generates a magnetic field?
James Clerk Maxwell.
What do Maxwell’s equations and the Lorentz force formula express?
The basic laws of electromagnetism.
What do Maxwell’s equations predict about electromagnetic waves?
They are coupled time-varying electric and magnetic fields propagating through space.
What speed did Maxwell predict for electromagnetic waves?
Close to 3 × 10^8 meters per second.
What conclusion was drawn from the predicted speed of electromagnetic waves?
That light is an electromagnetic wave.
Who experimentally demonstrated electromagnetic waves in 1885?
Heinrich Hertz.
What technological use of electromagnetic waves led to modern communication?
Their use by Marconi and others.
What is displacement current associated with?
A time-varying electric field.
What formula gives displacement current?
i_d = ε₀ dΦ_E/dt.
Why does electric flux change during capacitor charging?
Because the plate charge changes.
What equals the displacement current during capacitor charging?
The conduction current in the connecting wire.
What are conduction and displacement currents outside capacitor plates?
i_c = i and i_d = 0.
What are conduction and displacement currents between capacitor plates?
i_c = 0 and i_d = i.
What magnetic effects does displacement current have?
The same physical magnetic effects as conduction current.
Can displacement current exist where there is no conduction current?
Yes, it can exist without conduction current.
What is the total current composed of in the Ampere–Maxwell law?
The sum of conduction and displacement currents.
What formula expresses the total current including displacement current?
i = i_c + ε₀ dΦ_E/dt.
What does the Ampere–Maxwell law state about magnetic field circulation?
It equals μ₀ times the sum of conduction and displacement currents.
What is the integral form of the Ampere–Maxwell law?
∮ B · dl = μ₀ (i_c + ε₀ dΦ_E/dt).
Which four equations make up Maxwell's vacuum equations?
Gauss’s laws for electricity and magnetism, Faraday’s law, and Ampere–Maxwell law.
Why is the symmetry between Faraday’s and Ampere–Maxwell laws incomplete?
Because no magnetic monopoles analogous to electric charges are known.
What fields do stationary charges produce?
Electrostatic fields.
Do charges in uniform motion produce electromagnetic waves?
No, they produce magnetic fields that do not vary with time and no electromagnetic waves.
What does an oscillating charge produce?
An oscillating electric field that produces an oscillating magnetic field.
How do oscillating electric and magnetic fields interact in wave propagation?
They regenerate each other as the wave propagates.
What equals the frequency of an electromagnetic wave from an oscillating charge?
The oscillation frequency of the charge.
Who produced and detected electromagnetic waves in 1887?
Hertz.
In which year did Hertz produce and detect radio-wave electromagnetic waves?
1887.
Why did Hertz produce electromagnetic waves in the radio-wave region?
Because electronic circuits could not oscillate at the frequency of yellow light (~6×10¹⁴ Hz).
How are the electric field, magnetic field, and propagation direction oriented in a plane electromagnetic wave?
They are mutually perpendicular.
What is the expression for the electric field in a wave propagating in the z-direction?
E_x = E_0 sin(kz - ωt).
What is the expression for the magnetic field in a wave propagating in the z-direction?
B_y = B_0 sin(kz - ωt).
How is the wave number k related to the wavelength λ?
k = 2π / λ.
What is the common phase of the oscillating fields in the wave?
kz - ωt.
How are the amplitudes of the electric and magnetic fields related?
B_0 = E_0 / c.
What is the formula for electromagnetic wave speed in vacuum?
c = 1 / √(μ₀ε₀)
What is the approximate speed of electromagnetic waves in vacuum?
3 × 10⁸ meters per second
Which equation relates frequency, wavelength, and speed of electromagnetic waves?
νλ = c
How is the speed of electromagnetic waves in a material medium calculated?
v = 1 / √(με)
Can electromagnetic waves propagate through vacuum without a material medium?
Yes, they can propagate through vacuum without a material medium.
What do electromagnetic waves carry from one place to another?
Energy
Which types of waves are included in the electromagnetic spectrum?
Gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, and radio waves.
Do adjacent regions in the electromagnetic spectrum have sharp boundaries?
No, there are no sharp boundaries between adjacent regions.
Do all electromagnetic waves in vacuum travel at the same speed?
Yes, all electromagnetic waves in vacuum have the same speed.
Do electromagnetic waves differ in wavelength and frequency in vacuum?
Yes, their wavelengths and frequencies differ.
What is the approximate shortest wavelength in the electromagnetic spectrum?
About 10^-12 meters for gamma rays.
What is the approximate longest wavelength in the electromagnetic spectrum?
About 10^6 meters for long radio waves.
How are radio waves produced?
By accelerated electrons in conducting wires.
What frequency range do microwaves have?
Microwaves have frequencies in the gigahertz range.
Which devices produce microwaves?
Klystrons, magnetrons, or Gunn diodes produce microwaves.
What produces infrared waves?
Hot bodies and molecular vibrations produce infrared waves.
What frequency range does visible light occupy?
Visible light occupies approximately 4×10^14 Hz to 7×10^14 Hz.
What wavelength range corresponds to visible light?
Visible light wavelengths range from about 700 nm to 400 nm.
What wavelength range do X-rays have?
X-rays have wavelengths from about 10 nm to 10^-4 nm.
How are gamma rays produced?
Gamma rays are produced by nuclear reactions and radioactive nuclei.
Test your knowledge with 23 questions on Electromagnetic Waves.
1. What electromagnetic relationship did Maxwell add to complement Faraday’s law?
2. What do Maxwell’s equations together with the Lorentz force formula provide?
Review the complete course in the revision sheet for Electromagnetic Waves.
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