Electric field density at the surface of a current carring wire

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SUMMARY

The discussion focuses on calculating the electric and magnetic energy densities at the surface of a 3.0 mm diameter copper wire carrying a 15-A current. The relevant equations include magnetic energy density, uB = 0.5 * (B^2 / μ0), and electric energy density, uE = 0.5 * (ε0 * E^2). The user encounters difficulties with the electric energy density calculation, particularly with the electric field strength, E = V/d, where d approaches zero at the wire's surface, leading to an undefined scenario. The user seeks clarification on resolving this issue and understanding the implications of infinite electric field strength.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically electric and magnetic fields.
  • Familiarity with the equations for energy density in electromagnetic fields.
  • Knowledge of Ohm's Law and resistance calculations.
  • Basic principles of current-carrying conductors, particularly copper wire properties.
NEXT STEPS
  • Study the concept of electric fields around conductors, particularly at the surface of wires.
  • Learn about the implications of singularities in electric field calculations.
  • Explore the relationship between current, voltage, and resistance in conductive materials.
  • Investigate the physical significance of energy densities in electromagnetic fields.
USEFUL FOR

Students and professionals in physics, electrical engineering, and anyone involved in electromagnetic theory or applications related to current-carrying conductors.

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Homework Statement


Calculate the magnetic and electric energy densities at the surface of a 3.0 mm diameter copper wire carrying a 15-A current



Homework Equations


uB=.5[tex]\frac{B<sup>2</sup>}{\mu<sub>0</sub>}[/tex]
uE=.5[tex]\epsilon<sub>0</sub>[/tex]E2
R=[tex]\rho[/tex](L/A)
B=([tex]\mu<sub>0</sub>[/tex]I)/(2[tex]\pi[/tex]r)
[tex]\rho[/tex]=1.68 x 10^-8 ohm-meters

The Attempt at a Solution


Okay, so finding the magnetic energy density isn't too difficult. My problem is with the electric energy density. I can use the area of the wire and the fact that it's copper to find the resistance and then use ohm's law to find the voltage. but then I get in this bind. E=V/d, but at the surface of the wire, d=0 so you get V/0 which kind of implies infinity and this agrees with my thoughts anyway. However, I feel like this doesn't really make any sense in terms of an electric energy density. Does some one see where the reasoning is going wrong and how I can make it right?
 
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whoa...okay the equations got screwed up there. Hope you can understand them...B^2 is obviously the one in magnetic energy density, mu sub zero, E^2. Sorry about that folks.
 
I've just realized that the same problem comes up with my magnetic field. So. Basically I have no idea what I'm doing and am in need of desperate help.
 

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