What is the difference between method of images (mi) , separation of variables (sv) and multipole...

What is the difference between method of images (mi) , separation of variables (sv) and multipole expansion(me) ? What are the signs that a problem is under mi, sp and me? What solution will i use for each? Thank you!

Expert Solution

The method of images is used to find field due to grounded conducting plane and a free charge. The situation is similar to an image charge with the same source charge.

In separation of variables problem, we solve Laplace's equation directly. In that case, the potential dependent variables are identified and then integrating with respect to them using separation of variables method.

In the multipole expansion, we use infinite series sum to find the potential due to an arbitrary charge distribution. This method is superior to all methods and it give better approximation as we go very far from the source.

To identify a problem to be mi, me or sv:

1. If the problem contains grounded conductor (plane or sphere normally) and a source, we can use mi.

2. If the potential at boundaries are specified and it is possible to find a coordinate system to suite with the problem, we can use sv.

3. If the field point is very far from the source and we have to find the potential or field, we can use me. Then expand the potential as an infinite series of Legendre polynomials.

genius_generous answered 2 years ago

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