Suppose that charges on a dipole antenna oscillate slowly at...

Suppose that charges on a dipole antenna oscillate slowly at a rate of 1.00 cycle/s, and the antenna radiates electromagnetic waves in a region of space. If someone measured the time-varying magnetic field in the region and found its maximum to be $1.00 \mathrm{mT}$, what would be the maximum electric field, $E$, in the region, in units of volts per meter? What is the period of the charge oscillation? What is the magnitude of the Poynting vector?

Key Concepts

Electromagnetic Waves

Electromagnetic waves consist of oscillating electric and magnetic fields that propagate through space at the speed of light. In a wave, the magnitudes of the electric field (E) and the magnetic field (B) are related, and they are perpendicular to each other as well as to the direction of propagation. This concept underlies the propagation of energy and information in various applications, including radiating systems like antennas.

Relationship Between Electric and Magnetic Fields

Maxwell’s equations predict that in free space, the electric and magnetic fields of an electromagnetic wave are related by the speed of light, c, such that E = cB for wave propagation. This relationship allows one to determine one field component when the other is known, making it fundamental in characterizing the wave’s properties and its energy content.

Oscillation Frequency and Period

The oscillation frequency refers to the number of cycles per unit time at which a system, such as a dipole antenna, oscillates. The period of the oscillation is the inverse of the frequency, representing the time required to complete one full cycle. This concept is crucial for understanding temporal variations in systems and their associated wave phenomena.

Poynting Vector

The Poynting vector represents the directional energy flux (the rate of energy transfer per unit area) in an electromagnetic field. It is defined as S = E × B / ?0, where ?0 is the permeability of free space. The magnitude of the Poynting vector provides a measure of the intensity of the electromagnetic wave and is a key quantity in energy conservation and radiation studies.

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