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Chapter 25: Problem 1

lf the electric field in an electromagnetic wave is increasing in magnitude at a particular time, is the magnitude of the magnetic field at the same time increasing or decreasing? Explain.

Short Answer

Expert verified
The magnitude of the magnetic field is increasing.

Step by step solution

01

Understanding Electromagnetic Waves

Electromagnetic waves consist of both electric and magnetic fields which oscillate perpendicular to each other and the direction of wave propagation. If the electric field changes, it directly affects the magnetic field.
02

Maxwell's Equations Insight

According to Faraday's Law of Induction, a changing electric field induces a magnetic field. Specifically, if the electric field increases, it creates a time-varying magnetic field.
03

Relationship Between Fields

The oscillation of the electric field means the magnetic field also oscillates in sync but perpendicular to it. As the electric field increases, the associated magnetic field produced by it must also change proportionally.
04

Conclusion

At any given point where the electric field is increasing, by the laws governing electromagnetic waves, the magnitude of the magnetic field also increases. This is due to their interdependent oscillating nature.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Field
In physics, an electric field is a region around a charged particle where a force is exerted on other charged particles. The electric field is a vector field, which means it has both magnitude and direction.
In an electromagnetic wave, the electric field is constantly changing and oscillates in a direction perpendicular to the magnetic field. This oscillation is crucial because it allows the wave to propagate through space without needing a medium.
  • Electric fields are represented by lines. The closer the lines, the stronger the field.
  • The electric field's strength is measured in volts per meter (V/m).
  • The direction of the field lines indicates the direction of the force experienced by a positive test charge.
Understanding how electric fields work is essential to grasping how electromagnetic waves propagate, as they interact intimately with magnetic fields in these waves.
Magnetic Field
A magnetic field is a field that exerts a force on charges moving within it. It is perpendicular to the electric field in electromagnetic waves and also oscillates in its own plane.
The magnetic field in electromagnetic waves is crucial for maintaining wave propagation since it sustains the electric field through induction.
  • Unlike electric fields, magnetic fields are caused by moving charges, not stationary ones.
  • The SI unit of the magnetic field is the tesla (T).
  • Magnetic field lines form closed loops, showing the absence of magnetic monopoles.
The interaction and mutual oscillation of electric and magnetic fields ensure continuous wave motion, making them fundamental to understanding the nature of electromagnetic radiation.
Maxwell's Equations
Maxwell's Equations are a set of four fundamental equations that describe how electric and magnetic fields interact and behave. They are the foundation of classical electromagnetism, optics, and electric circuits.
  • Gauss's Law for electricity relates electric charge to electric field creation.
  • Gauss's Law for magnetism states that there are no magnetic monopoles.
  • Faraday's Law of Induction relates changing magnetic fields to electric fields.
  • Ampere-Maxwell Law links magnetic fields to electric currents and changing electric fields.
These equations show that a changing electric field can produce a magnetic field, which is essential for electromagnetic wave propagation. They intimately connect to the core principles guiding the behavior of electric and magnetic fields in various contexts.
Faraday's Law of Induction
Faraday's Law of Induction is part of Maxwell's Equations and explains the process of electromagnetic induction. It says that a changing magnetic field within a closed loop induces an electromotive force (EMF).
This is the principle that allows electric generators and transformers to work. In electromagnetic waves, this law implies that a changing electric field generates a magnetic field, maintaining the oscillation of the wave.
  • Faraday's Law mathematically is given by \( \text{EMF} = - \frac{d\Phi_B}{dt} \), where \( \Phi_B \) is magnetic flux.
  • The negative sign indicates the direction of the induced EMF is such that it opposes the change in magnetic flux.
  • This principle is essential for understanding how technologies like induction cooktops and wireless charging work.
Faraday's Law's ability to connect changing fields allows us to see how various components in electromagnetic waves coalesce to form a harmonious and stable wave structure.

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Most popular questions from this chapter

A typical home may require a total of \(2.00 \times 10^{3} \mathrm{kWh}\) of energy per month. Suppose you would like to obtain this energy from sunlight, which has an average daylight intensity of \(1.00 \times 10^{3} \mathrm{W} / \mathrm{m}^{2} .\) Assuming that sunlight is available \(8.0 \mathrm{h}\) per day, 25 d per month (accounting for cloudy days), and that you have a way to store energy from your collector when the Sun isn't shining, determine the smallest collector size that will provide the needed energy, given a conversion efficiency of \(25 \%\)

A \(65-k W\) radio station broadcasts its signal uniformly in all directions. (a) What is the average intensity of its signal at a distance of \(250 \mathrm{m}\) from the antenna? (b) What is the average intensity of its signal at a distance of \(2500 \mathrm{m}\) from the antenna?

Experiments show that the ground spider Drassodes cupreus uses one of its several pairs of eyes as a polarization detector, In fact, the two eyes in this pair have polarization directions that are at right angles to one another. Suppose linearly polarized light with an intensity of \(825 \mathrm{W} / \mathrm{m}^{2}\) shines from the sky onto the spider, and that the intensity transmitted by one of the polarizing eyes is \(232 \mathrm{W} / \mathrm{m}^{2}\) (a) For this eye, what is the angle between the polarization direction of the eye and the polarization direction of the incident light? (b) What is the intensity transmitted by the other polarizing eye?

The electric field of an electromagnetic wave points in the positive \(y\) direction. At the same time, the magnetic field of this wave points in the positive \(z\) direction. In what direction is the wave traveling?

The \(H_{\beta}\) line of the hydrogen atom's spectrum has a normal wavelength \(\lambda_{\beta}=486 \mathrm{nm}\). This same line is observed in the spectrum of a distant quasar, but lengthened by \(20.0 \mathrm{nm}\). What is the speed of the quasar relative to Earth, assuming it is moving along our line of sight?
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