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Chapter 22: Problem 9

An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?

Short Answer

Expert verified
Answer: The magnetic dipole antenna should be oriented vertically for optimal reception of the radio waves.

Step by step solution

01

Understand the behavior of electric dipole antennas

An electric dipole antenna generates an oscillating electric field along its axis when transmitting radio waves. In this case, the electric dipole antenna is oriented horizontally north-south, which means the electric field oscillates along the north-south direction. Consequently, the transmitted radio waves will have their electric fields aligned north-south as well.
02

Determine the direction of the magnetic field in the transmitted waves

Electromagnetic waves consist of oscillating electric and magnetic fields, which are always mutually perpendicular and orthogonal to the direction of propagation. In this case, since the electric field is oriented north-south and the wave is propagating in the east-west direction (due to the location of the receiving antenna being due east of the transmitter), the magnetic field in the transmitted waves must be oscillating vertically (up-down).
03

Understand the behavior of magnetic dipole antennas

A magnetic dipole antenna responds to the oscillating magnetic field in the radio waves. For the magnetic dipole antenna to serve as an effective receiver, it needs to be oriented in such a way that its axis is aligned with the direction of the magnetic field in the incoming waves.
04

Orient the magnetic dipole antenna as a receiver

Since the magnetic field in the transmitted waves is oscillating vertically (up-down), the magnetic dipole antenna should be oriented vertically as well. This will optimize the reception of the transmitted signal, as the antenna will be aligned with the direction of the magnetic field in the incoming waves. In conclusion, to effectively receive the radio waves transmitted by the horizontally north-south oriented electric dipole antenna, the magnetic dipole antenna should be oriented vertically at a point due east of the transmitter.

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Most popular questions from this chapter

The magnetic field of an EM wave is given by \(B_{y}=\) $B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,\( and \)B_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.
The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}\( and frequency \)3.0 \mathrm{MHz}$. (a) Find the amplitude and frequency of the electric field. (b) The wave is traveling in the \(-y\) -direction. At \(y=0\) and \(t=0\), the magnetic field is $1.5 \times 10^{-11} \mathrm{T}\( in the \)+z$ -direction. What are the magnitude and direction of the electric field at \(y=0\) and \(t=0 ?\)
An AM radio station broadcasts at \(570 \mathrm{kHz}\). (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is \(0.20 \mathrm{mH},\) what is the capacitance in the tuning circuit? (c) In the vicinity of the radio, the amplitude of the electric field is \(0.80 \mathrm{V} / \mathrm{m} .\) The radio uses a coil antenna of radius \(1.6 \mathrm{cm}\) with 50 turns. What is the maximum emf induced in the antenna, assuming it is oriented for best reception? Assume that the fields are sinusoidal functions of time.
A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .\( Light of wavelength \)480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?
In order to study the structure of a crystalline solid, you want to illuminate it with EM radiation whose wavelength is the same as the spacing of the atoms in the crystal \((0.20 \mathrm{nm}) .\) (a) What is the frequency of the EM radiation? (b) In what part of the EM spectrum (radio, visible, etc. \()\) does it lie?
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