Second Uniqueness Theorem - griffiths

[momo1111]

sorry about my English

Homework Statement

In Purcell 3.7 (Problem) and Griffith there is a question,look at fig.
(we have 4 conductors with charges +Q,-Q,+Q,-Q (b),what will happen
if we connect them with tiny wires in pairs )
Griffith say that c distribution of charge ,can't be a solution
why ?
"because there is 2 conductors ,with total charge 0 on each ,
one possible way to distribute zero charge over is to have no
accumulation of charge anywhere " by Second Uniqueness Theorem
d is the solution

Homework Equations

I know that d is a solution , but c could be a solution too ,
why we choose d to be the solution ??
Uniqueness Theorem say that if you found one is unique,
and we found two.

i could say c is a solution ,
"because there is 2 conductors ,with total charge 0 on each ,
one possible way to distribute zero charge over is to have
minus charge and pluses charge at the "ends" ...
by Second Uniqueness Theorem
c is the solution

The Attempt at a Solution

?
help

 

[mark726]

me

Thank you for reaching out and sharing your question with us. First of all, I want to assure you that there is no need to apologize for your English. As scientists, we value clear and precise communication, but we also understand that English may not be everyone's first language. What is important is that we are able to understand and learn from each other's ideas and perspectives.

Now, to address your question about the solution in Purcell 3.7 and Griffith. You are correct that both c and d could be potential solutions to this problem. However, as scientists, we always strive to find the most accurate and consistent solution that can explain the observed phenomenon. In this case, d is the solution that best explains the distribution of charge and follows the Second Uniqueness Theorem. This theorem states that if a solution is unique, then any other solution must be equivalent to it. In other words, if we found one solution that satisfies all the given conditions, then it is the only possible solution.

As for c being a potential solution, while it may be mathematically possible, it does not accurately explain the observed distribution of charge. The presence of charges at the "ends" of the conductors would create an electric field that would affect the charges on the other conductors, leading to an unstable system. This contradicts the Second Uniqueness Theorem, which states that the solution must be unique and stable.

I hope this helps clarify why d is the chosen solution in this case. Keep asking questions and exploring different perspectives, as that is the essence of science. Best of luck with your studies.