I need to solve laplace's equation in 2-d polar co-ordinates, and I just get the standard V(r,theta) = A + Blnr + sum to infinity of [An*sin(n*theta) + Bn * cos(n*theta)]*[Cn*(r^-n) + Dn*(r^n)](adsbygoogle = window.adsbygoogle || []).push({});

by using separation of variables and considering all values of the separation constant which give sinusoids in theta, and also letting the separation constant equal zero. N.b A,B,An,Bn,Cn,Dn are all constant.

I need to impose boundary conditions

1) V Tends to zero as r tends to infinity (i.e A=Dn=0)

2) for r=a V=2V1*theta/pi for -pi/2<theta<pi/2

V=2V1*(1-theta/pi) for pi/2<theta<3pi/2

where v1 is a constant

I know that I need to use a fourier series but because V(a) does not have its centre at the origin, the algerba is messy and doesn't really go anywhere. The only way I can think of solving this problem is to translate V(a) so that it is symmetric about the origin, take the fourier cosine series, and then translate it back using the substitution theta = theta + pi/2. Is this the correct way of doing it?

Thanks very much

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# Homework Help: Laplace's eqn

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