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## A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.30 m and consists of 420 turns. The

Question

A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.30 m and consists of 420 turns. The transmitted radio wave has a frequency of 1.3 MHz. The magnetic field of the wave is parallel to the normal of the coil and has a maximum value of 1.7 x 10-13 T. Using Faraday’s Law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna in this time.

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Physics
1 year
2021-08-31T14:50:59+00:00
2021-08-31T14:50:59+00:00 1 Answers
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## Answers ( )

Answer:The average emf induce is [tex]V = 2.625 * 10^{-5} \ V[/tex]

Explanation:From the question we are told that

The radius of the coil is [tex]r = 0.30 \ m[/tex]

The number of turns is [tex]N = 420 \ turns[/tex]

The frequency of the transition radio wave is [tex]f = 1.3\ MHz = 1.3 *10^{6} Hz[/tex]

The magnetic field is [tex]B_,{max} = 1.7 * 10^{-13} \ T[/tex]

The time taken for the magnetic field to go from zero to maximum is [tex]\Delta T = \frac{T}{4}[/tex]

The period of the transmitted radio wave is [tex]T = \frac{1}{f}[/tex]

So

[tex]\Delta T = \frac{T}{4} = \frac{1}{4 f}[/tex]

The potential difference can be mathematically represented as

[tex]V = NA (\frac{\Delta B}{\Delta T} )[/tex]

[tex]V = NA ([B_{max} – B_{min} ] * 4f)[/tex]

Where [tex]B_{min} = 0T[/tex]

substituting values

[tex]V = 420 * (\pi *(0.30)^2) * (1.7 *10^{-13} * 4 * 1.3 *10^{6})[/tex]

[tex]V = 2.625 * 10^{-5} \ V[/tex]