How Do Symmetry, Uniqueness, and Superposition Solve Electrostatic Problems?

[Welshy]

Homework Statement

Past exam question:
Briefly explain the roles of symmetry, uniqueness and superposition in solving electrostatics problems.

Homework Equations

N/A

The Attempt at a Solution

I know the definition of these words and could cobble together an answer from that - but is there anything particular that they might have been looking for?

 

[Hootenanny]

Homework Statement

Past exam question:
Briefly explain the roles of symmetry, uniqueness and superposition in solving electrostatics problems.

Homework Equations

N/A

The Attempt at a Solution

I know the definition of these words and could cobble together an answer from that - but is there anything particular that they might have been looking for?

Often the best way of answering such questions is to ask "what would happen if the principle of X didn't hold? How would I go about solving a problem?".

This should help you explain the roles of the principles involved.

 

[Welshy]

Often the best way of answering such questions is to ask "what would happen if the principle of X didn't hold? How would I go about solving a problem?".

This should help you explain the roles of the principles involved.

Edit: Found it! Thanks.

 

[Hootenanny]

Thanks. That helps with symmetry and superposition. But how does uniqueness figure into that - and even electrostatics for that matter?

Okay, say that you have found a solution for a particular electrostatics problem using a particular method. This solution will give you the value of the electric field at any point in space.

No suppose you use a different method and obtain a different solution. This solution also gives the value of the electric field at any point in space. However, since this solution is different to the first, it may also give you different values for the electric field.

How can this be?