Calculating Electron Motion in an AM Radio Broadcasting Circuit

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SUMMARY

The discussion focuses on calculating electron motion in an AM radio broadcasting circuit operating at a frequency of 550 kHz. For part (a), the time period for one complete cycle is determined to be approximately 1.818 microseconds (μs). In part (b), the range of motion of the electrons, given their average speed of 100 μm/s, requires understanding that they travel their full range in half a cycle. The correct calculation for the range of motion results in a value of 90.9 nm, but the initial attempt yielded an incorrect answer due to a misunderstanding of the conversion between units.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with frequency and period calculations
  • Basic knowledge of electron speed and motion
  • Ability to convert units (e.g., from μm to nm)
NEXT STEPS
  • Review calculations involving frequency and time period in oscillatory systems
  • Study the principles of simple harmonic motion in electrical circuits
  • Learn about electron mobility and speed in conductive materials
  • Practice unit conversions, particularly between micrometers and nanometers
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Students studying physics, electrical engineering, or anyone interested in the dynamics of electron motion in circuits, particularly in the context of AM radio broadcasting.

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Homework Statement


Consider the broadcasting circuit for an AM radio station which broadcasts at a frequency of 550 kHz. The electrons in such a circuit are moving back and forth in simple harmonic motion.

(a) How long does it take for the free electrons in this circuit to go back and forth once? Give your answer in μs.


(b) Assuming the average speed of the electrons is 100 μm/s, what is the range of motion of the electrons as they go back and forth in the wires of the circuit. (HINT: As the electron goes back and forth, it travels its full range every half cycle.) Give your answer in nm.
nm



Homework Equations


T=s/cycles
d=vt?


The Attempt at a Solution



the answer to a was easy - just the reciprocal of 550khz.

b, seems a little more confusing. I know the speed (100x10^-6) of the electrons, and the time (answer a), but my confusion is in the "hint". Would I multiply the time by 2?

Thank you!
 
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The hint is telling you that the electrons are traveling the full range of motion in 1/2 of a period.
 
Ok, so I multiplied v(100x10^-6) by (1/2)(1.818x10^-6) and got 9.09x10^-11. It asks for the answer in nm (^-9), so I entered 90.9, and it was incorrect. Can someone tell me what I am doing wrong? I only have 1 attempt left.
 

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