Current required in a long wire

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SUMMARY

The discussion focuses on calculating the current required in a long straight wire to generate a magnetic field with an amplitude equivalent to that of an electromagnetic wave carrying a flux density of 100 mW/cm². The magnetic field amplitude was determined to be 2.89 x 10-6 T. The relevant equation used is $$B_0=\frac{E_0}{c}=\frac{1}{c}\sqrt{\frac{2I}{c\epsilon_0}}$$, where 'c' is the speed of light and 'ε0' is the permittivity of free space. The discussion highlights the need for further clarification on the current calculation process.

PREREQUISITES
  • Understanding of electromagnetic wave properties
  • Familiarity with the equations of electromagnetism, specifically Maxwell's equations
  • Knowledge of the speed of light (c) and permittivity of free space (ε0)
  • Basic proficiency in solving equations involving magnetic fields and currents
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  • Research the derivation of the equation $$B_0=\frac{1}{c}\sqrt{\frac{2I}{c\epsilon_0}}$$
  • Study the relationship between current and magnetic field strength in long straight wires
  • Explore the concept of electromagnetic wave flux density and its implications
  • Learn about the practical applications of electromagnetic theory in engineering
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Students in physics or electrical engineering, educators teaching electromagnetism, and professionals working with electromagnetic wave applications.

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Homework Statement



Determine the amplitude of a magnetic field in an electromagnetic wave that carries a flux density of 100 mW/cm2. How much current would be required in a long straight wire so that the magnetic field if this same amplitude would be generated at a distance of 1mm from the wire.

Homework Equations



$$B_0=\frac{E_0}{c}=\frac{1}{c}\sqrt{\frac{2I}{c\epsilon_0}}$$

The Attempt at a Solution



I'm not sure how to get at this one. I got that $$B_0=2.89 \cdot 10^{-6} T.$$ Just a touch in the right direction would be awesome.
 
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The approach looks fine, and a computer can check the numerical value. Where is the problem?
 

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