An 800 kHz radio signal is detected at a point 1.1 km distant from a transmitter tower. The...

Question:

An 800 kHz radio signal is detected at a point 1.1 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 110 mV/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. The magnetic field amplitude of the signal at that point, in nT, is?

Radio Signals:

The waves having the frequency limit equal to radio waves and used for the transmission of electronic signals and messages to the wireless devices are known as radio signals. While traveling, these waves exhibit both electric and magnetic fields.

Answer and Explanation: 1


Given Data

  • The frequency of radio signal is: {eq}{f_r} = 800\;{\rm{kHz}} = 800 \times {10^3}\;{\rm{Hz}} {/eq}.
  • The distance of the point from the transmission tower is: {eq}x = 1.1\;{\rm{km}} = 1100\;{\rm{m}} {/eq}.
  • The amplitude of the electric field at point is: {eq}{F_E} = 110\;{\rm{mV/m}} = 0.110\;{\rm{V/m}} {/eq}.


The expression to calculate the magnetic field amplitude of the signal at the point is given by,

{eq}{F_B} = \dfrac{{{F_E}}}{{{V_L}}} {/eq}

Here, {eq}{V_L} {/eq} is the speed of light, having a standard value of {eq}3.0 \times {10^8}\;{\rm{m/s}} {/eq}.


Substitute all the values in the above expression.

{eq}\begin{align*} {F_B} &= \dfrac{{0.110}}{{3.0 \times {{10}^8}}}\\ & = 0.366 \times {10^{ - 9}}\;{\rm{T}}\\ & = 0.366 \times {10^{ - 9}}\;{\rm{T}} \times \left( {\dfrac{{{{10}^9}\;{\rm{nT}}}}{{1\;{\rm{T}}}}} \right)\\ & \approx 0.37\;{\rm{nT}} \end{align*} {/eq}


Thus, the magnetic field amplitude of the signal at the point is {eq}0.37\;{\rm{nT}} {/eq}.


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Magnetic Forces & Fields Practice Problems

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Chapter 18 / Lesson 7
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Magnetism and electricity are closely related. When current flows in a wire, a magnetic field is generated. In this lesson, we will explore how magnetic fields can exert forces on parallel current-carrying wires.


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