ElectromagnetismLesson 1 of 4 in the course Electromagnetic Waves

Maxwell’s Equations, Electromagnetic Waves, and Hertz’s Experiments

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

This lesson explains why the original form of Ampère’s law was incomplete and how Maxwell’s displacement current resolves the problem. The idea is essential to understanding how changing electric fields can produce magnetic fields.

∮CB⋅dl=μ0I\oint_C \mathbf{B}\cdot d\mathbf{l}=\mu_0 I

A loop can bound many different surfaces. For a wire connected to a charging parallel-plate capacitor, choose one surface that cuts through the wire. It encloses the conduction current II. Choose another surface that bulges between the capacitor plates. No charges cross the gap, so this surface encloses no conduction current. The original law would then assign two different values to the same magnetic-field integral.

All flashcards

What is electric flux?
The surface integral of the electric field over an area: ΦE=∫SE⋅dA\Phi_E=\int_S\mathbf{E}\cdot d\mathbf{A}.
What is displacement current?
The contribution to magnetic-field production associated with changing electric flux: Id=ϵ0 dΦE/dtI_d=\epsilon_0\,d\Phi_E/dt.
Why does the original Ampère’s law fail for a charging capacitor?
Different surfaces with the same boundary can enclose different conduction currents, although the magnetic-field integral must be unique.
How do displacement and conduction currents compare in an ideal charging capacitor?
They are equal at each instant; both are (V0/R)e−t/RC(V_0/R)e^{-t/RC} in the stated RC circuit.
What experimental evidence showed that Hertz’s radiation behaved as a wave?
Hertz observed reflection, refraction, and interference.

Quiz questions

  1. What does Gauss’s law for magnetism state about the net magnetic flux through a closed surface?Answer: It is zero for every closed surface.
  2. What does the minus sign in Faraday’s law express?Answer: The induced effect opposes the change in magnetic flux.
  3. For a charged particle moving with velocity v\mathbf{v} in a magnetic field B\mathbf{B}, what is the direction of the magnetic part of the Lorentz force?Answer: Perpendicular to both the velocity and the magnetic field.
  4. For an RLC circuit with inductance LL and capacitance CC, what is its resonant frequency?Answer: f0=12πLCf_0=\frac{1}{2\pi\sqrt{LC}}.
  5. How can the speed of a wave be calculated from its frequency and wavelength?Answer: Multiply frequency by wavelength: v=fλv=f\lambda.

Based on University Physics Volume 2 by Samuel J. Ling, William Moebs, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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