Electric and Magnetic Fields in Capacitors
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Questions and Answers

What direction does the electric field Ex oscillate in for the described electromagnetic wave?

  • z-axis
  • along the wave propagation direction
  • x-axis (correct)
  • y-axis

    • What relationship does the wave number k have with the wavelength λ in electromagnetic waves?

  • k = c / λ
  • λ = k^2
  • k = 2π/λ (correct)
  • λ = 1/k

    • Which of the following statements about the electric and magnetic fields in an electromagnetic wave is true?

  • They both vary with time at the same rate.
  • They oscillate in the same direction.
  • They propagate in different media.
  • They are perpendicular to each other. (correct)

    • In the equation Ex = E0 sin(kz - ωt), what does E0 represent?

    <p>The electric field's peak value.</p> Signup and view all the answers

    What does the variable ω represent in the equations for Ex and By?

    <p>Angular frequency of the wave.</p> Signup and view all the answers

    Which of the following is true about the propagation of the electromagnetic wave described?

    <p>It propagates along the z-axis.</p> Signup and view all the answers

    How do the electric field Ex and the magnetic field By vary in space?

    <p>They vary sinusoidally with z.</p> Signup and view all the answers

    What does the frequency of an electromagnetic wave correspond to?

    <p>The frequency of oscillation of the charge</p> Signup and view all the answers

    What do the coordinates of the wave's fields indicate at a given time t?

    <p>The instantaneous values of the fields.</p> Signup and view all the answers

    What is a reason that testing the prediction that light is an electromagnetic wave is challenging?

    <p>The frequency of visible light is higher than available circuit frequencies</p> Signup and view all the answers

    Which experiment successfully demonstrated the existence of electromagnetic waves?

    <p>Hertz’s experiment</p> Signup and view all the answers

    What range of frequencies did Jagdish Chandra Bose work with in his experiments?

    <p>25 mm to 5 mm wavelength</p> Signup and view all the answers

    What results from the oscillation of the charge in electromagnetic wave propagation?

    <p>The regeneration of electric and magnetic fields</p> Signup and view all the answers

    Why could earlier experiments focus on the low-frequency region for electromagnetic waves?

    <p>Modern circuits could not achieve higher frequencies</p> Signup and view all the answers

    What overall impact did Hertz's experiment have on the field of physics?

    <p>It sparked further research into electromagnetic waves</p> Signup and view all the answers

    What form of energy is associated with the propagation of electromagnetic waves?

    <p>Energy from the accelerated charge</p> Signup and view all the answers

    Under what condition may the displacement current be zero?

    <p>When the electric field does not change with time</p> Signup and view all the answers

    What may exist in regions of space where there is no conduction current?

    <p>Only displacement current</p> Signup and view all the answers

    What is the relationship between a changing magnetic field and electrical phenomena?

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

    What observation can be made about the displacement current's effect?

    <p>It creates symmetry between electric and magnetic laws</p> Signup and view all the answers

    What does Faraday’s law of induction imply when there is an induced emf?

    <p>It implies the existence of an electric field</p> Signup and view all the answers

    In which situation are both conduction and displacement currents likely present?

    <p>In a charging capacitor</p> Signup and view all the answers

    What is the expression for the total current $i$ in a parallel plate capacitor?

    <p>$i = i_c + i_d$</p> Signup and view all the answers

    What happens to the conduction current $i_c$ inside the parallel plate capacitor?

    <p>$i_c$ equals zero.</p> Signup and view all the answers

    What can be experimentally verified regarding the displacement current?

    <p>It can lead to a measuring magnetic field in absence of conduction current</p> Signup and view all the answers

    What can be inferred about perfect conductors and insulators in the context of conduction and displacement currents?

    <p>Neither can perfectly isolate conduction or displacement currents</p> Signup and view all the answers

    What does the displacement current $i_d$ equal inside the capacitor?

    <p>$i_d$ is equal to the total current $i$.</p> Signup and view all the answers

    Which equation represents the generalized Ampere's circuital law?

    <p>$∫ B g d l = \mu_0 i_c + \mu_0 \epsilon_0 \frac{dΦ_E}{dt}$</p> Signup and view all the answers

    What is the role of the displacement current in a parallel plate capacitor?

    <p>It produces magnetic fields similar to conduction current.</p> Signup and view all the answers

    What does the term $\frac{dΦ_E}{dt}$ in the expression for displacement current represent?

    <p>It is the rate of change of electric field.</p> Signup and view all the answers

    Where is the conduction current only present in a parallel plate capacitor?

    <p>Outside the capacitor plates.</p> Signup and view all the answers

    Which statement best describes the displacement current $i_d$?

    <p>It arises from changing electric fields in a non-conducting medium.</p> Signup and view all the answers

    What is the primary function of microwaves in microwave ovens?

    <p>To match the resonant frequency of water molecules</p> Signup and view all the answers

    What is often referred to as heat waves?

    <p>Infrared waves</p> Signup and view all the answers

    What role do infrared radiation play in the greenhouse effect?

    <p>They trap heat that is re-radiated from the Earth's surface</p> Signup and view all the answers

    Which of the following wavelengths corresponds to visible light?

    <p>400-700 nm</p> Signup and view all the answers

    What happens to molecules when they absorb infrared waves?

    <p>They gain energy and their thermal motion increases</p> Signup and view all the answers

    What is one common use of infrared radiation mentioned?

    <p>Physical therapy</p> Signup and view all the answers

    What frequency range does visible light fall under?

    <p>$4 × 10^{14}$ Hz to $7 × 10^{14}$ Hz</p> Signup and view all the answers

    What distinguishes different animals' sensitivity to wavelengths?

    <p>The structure of their eyes</p> Signup and view all the answers

    Study Notes

    Electric and Magnetic Fields in Capacitors

    • Uniform electric field exists between parallel plate capacitor plates, generating both electric and magnetic fields.
    • Maxwell's generalization states that magnetic fields arise not only from conduction electric currents but also from changing electric fields.
    • Total current, i, consists of conduction current (ic) and displacement current (id), given by the equation:
      ( i = i_c + i_d = i_c + ε_0 \frac{dΦ_E}{dt} )

    Displacement Current

    • Outside capacitor plates, only conduction current exists (id = 0); inside, only displacement current exists (ic = 0).
    • Generalized Ampere’s circuital law combines conduction and displacement currents: ( \int B_g dl = μ_0 i_c + μ_0 ε_0 \frac{dΦ_E}{dt} )
    • Displacement current has identical effects to conduction current, crucial for explaining electric-magnetic interactions.

    Implications of Displacement Current

    • There are regions with only displacement current generated by time-varying electric fields, producing magnetic fields despite no conduction current sources.
    • Experimentation verifies predictions of displacement current; measurements show magnetic fields between capacitor plates match conditions outside.
    • Observations highlight increased symmetry in electricity and magnetism, linking time-varying electric and magnetic fields through electromagnetic wave propagation.

    Electromagnetic Waves

    • Electromagnetic waves comprise oscillating electric and magnetic fields that regenerate each other during propagation.
    • Frequency of these waves corresponds with the oscillation of charges; energy in waves comes from the source's energy.
    • Challenges arise in generating visible light frequencies (e.g., yellow light at 6 × 10^14 Hz) using conventional electronic circuits, which max out around 10^11 Hz.

    Historical Experiments

    • Hertz’s 1887 experiment confirmed Maxwell’s theory using low-frequency electromagnetic waves (e.g., radio waves).
    • Jagdish Chandra Bose further advanced the field by generating shorter wavelength electromagnetic waves in laboratory settings.

    Description of Electromagnetic Waves

    • Typical electromagnetic waves propagate with electric field ( E_x ) along the x-axis and magnetic field ( B_y ) along the y-axis, both varying sinusoidally:
      • ( E_x = E_0 \sin(kz - ωt) )
      • ( B_y = B_0 \sin(kz - ωt) )
    • These waves are central to applications like microwave ovens, where specific frequencies efficiently heat water molecules in food.

    Infrared Waves

    • Produced by hot objects and molecules, infrared waves are adjacent to the longest wavelengths of visible light.
    • Known as heat waves, they significantly heat substances (e.g., water) upon absorption, which increases thermal motion.
    • Used therapeutically in infrared lamps; essential for earth's thermal regulation through the greenhouse effect.

    Visible Light

    • Visible light forms the electromagnetic spectrum detected by the human eye, spanning approximately 4 × 10^14 Hz to 7 × 10^14 Hz (400 nm to 700 nm).
    • Provides information about the environment, with varying sensitivity across different animal species.

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    Description

    Explore the fascinating concepts of electric and magnetic fields within capacitors. This quiz delves into Maxwell's equations and the significance of displacement current in understanding electric-magnetic interactions. Challenge your knowledge about conduction and displacement currents and their implications in various scenarios.

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