Electric field density at the surface of a current carring wire

In summary, the task is to calculate the magnetic and electric energy densities at the surface of a 3.0 mm diameter copper wire carrying a 15-A current. The equations needed for this calculation are given as uB=.5(B^2)/mu0 for magnetic energy density and uE=.5*epsilon0*E^2 for electric energy density. The value of R, the resistance, can be found using the length and area of the wire and the resistivity of copper, which is 1.68 x 10^-8 ohm-meters. However, there is difficulty in finding the electric energy density due to the fact that at the surface of the wire, d=0, resulting in V/0 which
  • #1
cuttlefish
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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{B2}{\mu0}[/tex]
uE=.5[tex]\epsilon0[/tex]E2
R=[tex]\rho[/tex](L/A)
B=([tex]\mu0[/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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  • #2
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.
 
  • #3
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.
 

1. What is electric field density at the surface of a current carrying wire?

The electric field density at the surface of a current carrying wire is a measure of the strength of the electric field at a specific point on the surface of the wire. It is determined by the amount of current flowing through the wire and the distance from the surface.

2. How is the electric field density at the surface of a current carrying wire calculated?

The electric field density at the surface of a current carrying wire can be calculated using the formula E = I/2πr, where E is the electric field density, I is the current, and r is the distance from the surface. This formula is based on Ampere's Law.

3. Why is the electric field density at the surface of a current carrying wire important to know?

Knowing the electric field density at the surface of a current carrying wire is important for understanding the behavior of the electric field around the wire. It is also important for calculating the force exerted on other charges in the vicinity of the wire.

4. How does the electric field density change as the distance from the surface of the wire increases?

The electric field density decreases as the distance from the surface of the wire increases. This is because the electric field follows an inverse square law, meaning that the strength of the field decreases with the square of the distance.

5. Can the electric field density at the surface of a current carrying wire be altered?

Yes, the electric field density at the surface of a current carrying wire can be altered by changing the amount of current flowing through the wire or by changing the distance from the surface. It can also be affected by the presence of other charges or conductors nearby.

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