Hi, I have a maths exam tommorrow (!) and I'm stuck on something:(adsbygoogle = window.adsbygoogle || []).push({});

Its about solving LaPlace's equation in plane polar coordinates. There is a circular plate witha temp dist that satisfies

(1/r)(d/dr(r.df/dr)) + 1/r^{2}. d^{2}/dp^{2}= 0

(p is phi)

so I used a separable eq of the form f=RP

and solved it to get R = Cr^{m}+Dr^{-m}

when m doesn't equal 0

and R(r) = A + B ln(r)

when m=0

The question is:

What boundary condition does R(r) satisfy at r = 0? Use this to show that

the general solution to this problem is

f= A_{0 + SUM OF(rm)( Am cos(mp) + Bm sin(mp)) the explanation is because you can't have negative powers of m when R(r) is finite at the centre. Why can't you have negative powers of m? Negative powers will give fractions but they will still be finite, so why isn't it f= A0 + SUM OF(Cmrm+Dmr-m)( Am cos(mp) + Bm sin(mp)) Thanks if you can help before tommorrow!}

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# Temperature distribution on a circular plate

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