Designing a simple magnetic field gen with a straight wire. Need current density

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SUMMARY

The discussion focuses on designing a magnetic field generator using a solid metal wire with a specified current density, jw. The objective is to achieve a magnetic field strength of 7.5 x 10^-13 Tesla at a radial distance of 8mm from the wire's axis, with the wire having a radius of 2mm. The derivation begins with Ampere's Law, and the relevant equations include I=∫J*da and J=(I)/(∏*r*r). The user seeks guidance on correctly applying these equations to find the necessary current density.

PREREQUISITES
  • Understanding of Ampere's Law in electromagnetism
  • Familiarity with current density concepts
  • Knowledge of magnetic field calculations
  • Basic proficiency in calculus for integration
NEXT STEPS
  • Research the application of Ampere's Law in cylindrical coordinates
  • Study the relationship between current density and magnetic field strength
  • Explore the derivation of magnetic fields from current-carrying conductors
  • Investigate the effects of wire radius on magnetic field generation
USEFUL FOR

Students in physics or electrical engineering, particularly those focusing on electromagnetism and magnetic field applications, as well as hobbyists designing electromagnetic devices.

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Homework Statement


Need to design a simple magnetic field generator of radius a= 2mm. The solid metal wire must carry a current density, jw, uniformly distributed over its cross section. The current density that must be found must have a magnetic field at a radial distance of r= 8mm from the axis of the wire is 7.5 10^-13 Tesla. Ignore end effects. Must develop the equation using Ampere's Law as the beginning derivation.


Homework Equations


I=∫J*da
A=r*r*∏
B∫J*ds

The Attempt at a Solution



I am have been trying to start off this by drawing a diagram but I don't even think it is correct.

http://imageshack.us/photo/my-images/440/finalprep.png/
 
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Also I forgot an equation jw inside is

J=(I)/(∏*r*r)
 

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