Transportation of Charges and Energy Lost

[caduceus]

Homework Statement

http://img525.imageshack.us/img525/2069/spheressw9.jpg

At the initial picture, we have two spheres, such that,
the first one has charge Q, and the second one has no charge.

Then we connect these two spheres with a conducting wire and let some Q flow through the second sphere.

For the initial energy, we have;

Ei=Q$$^{2}$$/{8*pi*epsilon*a)}

For the final energy, after we did simple calculations, we have;

Ef={Q$$^{2}$$/(8*pi*epsilon)}*{1/(a+b)}

And then, we find energy lost, such that,

Ei-Ef={Q$$^{2}$$/(8*pi*epsilon)}*{b/[a*(a+b)]}

Then, we connected this energy lost to the resistance that the wire has.

However, if we suppose the wire does not have a resistance, then, how can we explain the energy lost here?

Homework Equations

Energy:
E=Q$$^{2}$$/(8*pi*epsilon*r), where r is the radius of the sphere.

Potential:
V=Q/(4*pi*epsilon*r), where r is the radius of the sphere.


Any comments will be appreciated.

 

[Jhero]

Thank you for sharing your thoughts on this interesting problem. I would like to offer my perspective on the energy lost in this scenario.

Firstly, it is important to note that the energy lost in this situation is not due to the resistance of the wire, but rather due to the transfer of charge between the two spheres. When the spheres are initially connected, there is a potential difference between them, which causes charge to flow from the charged sphere to the neutral one until they reach the same potential.

In this process, some energy is lost due to the work done in moving the charges against the electric field. This energy can be calculated using the formula E=QΔV, where Q is the charge transferred and ΔV is the potential difference between the two spheres.

Now, even if we consider a wire with zero resistance, there will still be a potential difference between the two spheres, and thus some energy will be lost in the transfer of charge. This energy loss is inherent in the process and cannot be completely eliminated.

I hope this explanation helps clarify the concept of energy lost in this scenario. If you have any further questions, please feel free to ask. Keep up the good work as a curious and inquisitive scientist!