Syed Wasif Mobin - 2000-12-04

Q1. Show that
μ(r, θ) = Brn  Sin nθ .
Satisfy the laplace equation in polar coordinate.

μ rr +1/r μ r + 1/r2 μ θ θ  = 0

Q2. A circular plate given by 0 <= r <= 1, &#960; <= &#952; <= &#960; kept at 50 Centigrade and a portion r =1 , -&#960; <= &#952; <= 0 kept at &#8211; 50 Centigrade, show that the steady state temp &#956; (in centigrade) at (r, &#952;) is given by &#956; (r, &#952;) = &#931; Bnrn sin n&#952;  ,  n= 1 to &#8734;
         Where Bn ={0    (even)
              {200/n&#960;  (odd)