What Is the Maximum EMF Induced in a Vibrating Guitar String?

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SUMMARY

The maximum electromotive force (emf) induced in a vibrating guitar string can be calculated using the formula Emf = BA, where B is the magnetic field strength and A is the area of the wire moving through the field. In this case, the wire has a linear density of 3.00 x 10-3 kg/m, is under a tension of 301 N, and is vibrating with an amplitude of 1.50 cm in a uniform magnetic field of 5.00 mT over a length of 2.00 cm. The correct approach to find the maximum emf involves differentiating the area with respect to time, leading to the equation Emf = d(BA)/dt.

PREREQUISITES
  • Understanding of electromagnetism principles, specifically Faraday's law of induction
  • Familiarity with the concepts of linear density and tension in strings
  • Knowledge of basic calculus for differentiation
  • Experience with magnetic fields and their effects on conductive materials
NEXT STEPS
  • Study Faraday's law of electromagnetic induction in detail
  • Learn about the relationship between tension, frequency, and amplitude in vibrating strings
  • Explore the effects of magnetic fields on moving charges and conductive materials
  • Practice solving problems involving induced emf in various configurations
USEFUL FOR

Physics students, electrical engineers, and educators looking to deepen their understanding of electromagnetic induction and its applications in vibrating systems.

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Homework Statement


Review problem. A flexible metallic wire with linear density 3.00 multiplied by 10-3 kg/m is stretched between two fixed clamps 64.0 cm apart and held under tension 301 N. A magnet is placed near the wire as shown in Figure P31.25. Assume that the magnet produces a uniform field of 5.00 mT over a 2.00 cm length at the center of the wire and a negligible field elsewhere. The wire is set vibrating at its fundamental (lowest) frequency. The section of the wire in the magnetic field moves with a uniform amplitude of 1.50 cm.

http://www.webassign.net/serpop/p23-18.gif

(b) Find the amplitude of the electromotive force (emfmax) induced between the ends of the wire.


Homework Equations



Emf = BA

The Attempt at a Solution



I am not quite sure I am doing the problem correctly. I had the area being 3.00cm X 2.00cm but that's not correct nor do I actually believe the above equation is the correct equation. I assume the equation needs to have a sine or a cosine in it, but we are needing to find Emfmax so that's not too important right? Thanks for the help.
 
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Correction to your equation:

<br /> Emf = \frac{d}{dt} (BA)<br />

Since B is constant, the problem comes down to finding dA/dt.
 

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