Uniqueness Theorem Homework: Static Charges in Vacuum

In summary, the uniqueness theorem for a system of static charges in a vacuum states that once a solution is found, it is the only solution. However, this may vary for different systems. A more explicit explanation is that if del^2 phi = - rho/epsilon_0 and del^2 psi = - rho/epsilon_0, then phi and psi are equal. This answer may be sufficient, but others may have differing opinions.
  • #1
captainjack2000
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Homework Statement


I have a situation with a charge distribution for a system of static charges in a vacuum. It then asks to state the uniqueness theorem for such a system.

Homework Equations





The Attempt at a Solution


I know that the uniquessness theorem means that once you have found one solution to the system you have found THE solution. But how does this change for different systems? Is this a good enoug answer to what is the uniqueness theorem?
 
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  • #2
perhaps you could be a little more explicit such as if we can find phi,psi such that del^2 phi = - rho/epsilon_0 and del^2 psi = - rho/epsilon_0 then phi=psi but id say it looks fine. perhaps someone else will disagree though...
 

1. What is the uniqueness theorem for static charges in vacuum?

The uniqueness theorem for static charges in vacuum states that the electric field in a vacuum region is uniquely determined by the distribution of static charges in that region.

2. How does the uniqueness theorem apply to electrostatics?

The uniqueness theorem is a fundamental principle in electrostatics that helps us understand the behavior of electric fields in vacuum regions. It states that for a given set of static charges, the electric field in a vacuum region is uniquely determined.

3. Can the uniqueness theorem be applied to non-vacuum regions?

No, the uniqueness theorem only applies to vacuum regions where there are no materials present. In non-vacuum regions, the presence of materials can affect the behavior of electric fields, making the theorem invalid.

4. How is the uniqueness theorem used in practical applications?

The uniqueness theorem is used in practical applications such as designing electrical devices and systems, calculating electric potential and field strength, and solving boundary value problems in electrostatics.

5. Are there any limitations to the uniqueness theorem in electrostatics?

Yes, the uniqueness theorem has some limitations. It only applies to static charges and cannot be used for time-varying situations. It also assumes ideal conditions, such as perfect conductors and an absence of external magnetic fields. In real-world scenarios, these assumptions may not hold true and can affect the accuracy of the theorem.

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