Conducting Wire Homework: Find J0 & B Inside Wire

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SUMMARY

The discussion focuses on calculating the constant J0 and the magnetic field strength B inside a long, straight conducting wire with a nonuniform current density defined as J=J0*r/R. The total current I is carried by the wire, and the user initially misapplies the formula J=I/A, leading to incorrect expressions for J0 and B. The correct expression for J0 is derived from integrating the current density over the cross-sectional area of the wire, while the magnetic field strength B is determined using Ampère's Law.

PREREQUISITES
  • Understanding of current density and its relation to total current
  • Familiarity with Ampère's Law and magnetic fields
  • Knowledge of calculus for integrating functions over areas
  • Basic concepts of cylindrical coordinates in physics
NEXT STEPS
  • Study the derivation of current density in nonuniform wires
  • Learn about Ampère's Law and its applications in electromagnetism
  • Explore integration techniques for calculating areas under curves
  • Investigate the properties of magnetic fields in cylindrical geometries
USEFUL FOR

Physics students, electrical engineers, and anyone studying electromagnetism and current distribution in conducting materials.

dtesselstrom
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Homework Statement


A long, straight conducting wire of radius R has a nonuniform current density J=J0*r/R, where J0 is a constant. The wire carries total current I.
Find an expression for J_0 in terms of I and R.
Find an expression for the magnetic field strength inside the wire at radius r.

Homework Equations


J=I/A
B*ds = u0*I

The Attempt at a Solution



So from my book it looks like J0=I/A which is Jo=I/(pi*R^2) which says it is off by a multiplication factor not sure where I am going wrong here. As for the second portion I got B= uo*I*r/(2*pi*R^2) which is also wrong so any help on this would be much helpful.
 
Physics news on Phys.org
Since J is a function of r, it will be constant for a thin cylindrical shell centered on the wire. Adding up the current in all these shells will equal I.
 

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