Electric field density at the surface of a current carring wire

AI Thread Summary
The discussion centers on calculating the magnetic and electric energy densities at the surface of a copper wire with a 3.0 mm diameter carrying a 15-A current. The user successfully identifies the formula for magnetic energy density but struggles with electric energy density due to the challenge of calculating voltage at the wire's surface, where the distance approaches zero, leading to an undefined electric field. The user expresses confusion over the implications of this scenario and seeks clarification on the reasoning behind the calculations. Additionally, there is a realization that similar issues arise with the magnetic field calculations. Overall, the user is looking for guidance to resolve these conceptual difficulties in their homework.
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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\frac{B<sup>2</sup>}{\mu<sub>0</sub>}
uE=.5\epsilon<sub>0</sub>E2
R=\rho(L/A)
B=(\mu<sub>0</sub>I)/(2\pir)
\rho=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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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