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Simon Bridge
Dec5-12, 01:22 AM
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The electric field depends on a distribution of charges - but the distribution of charges depends on the electric field. This creates a chicken-and-egg situation.

A "self consistent" field is one which makes the charges distributed so that they generate the field. We can compute them using an iterative procedure.

You start with a guess for a charge distribution ρ0, compute the field that distribution gives rise to. That field will push the charges into a new configuration ρ' - so work out that new distribution as if the field were fixed at what you calculated.

Now repeat the procedure for ρ1=(1-λ)ρ0+λρ' where 0<λ<1.
You have to guess lambda.

Keep going until you keep getting the same result to the desired level of accuracy.

The exact method will depend on the context.