Tiong thanh khOng c6 ngu6n nhiOt, hai ddu mrit ctra thanh luOn dugc gifr 6 nhiet dQ bang khOng.. 86 qua su ffao Cdi ntriet qua mdt b0n, vdn tdc truydn nhigt ffong thanh bdng a.. X€t hinh
Trang 1n0 crAo DUc VA DAo TAo Hq vd t€n thi sinh:
KV rHI ruyfx srNH sAU DAI Hoc NAM 2006
MOn thi: To6n cho vilt ly (ddnh cho: Cao hgc) Thdi gian ldm bdi: 180 phtit CAU 1 Tim hbm u(r,y) th6a mdn phuong fiinh
0 2 u ^ 0'u 0 ' u ^
a * r - " a r a a - o 6 r z : v
vi th6a m6n cdc didu kiOn
u(r, a)lr:o : 3r2 ,
Hlr:o : O.
Ctllu 2 Tim phAn b0 nhi0t dE u(r,t) trong mQt thanh htru han c6 chidu ddi (, tat thdi didm bat ky t > 0 BiCt rang phAn bd nhiet d0 ban ddu trong thanh c6 dang u(r,,O) : Ar((, - r), (A li hang s0) Tiong thanh khOng c6 ngu6n nhiOt, hai ddu mrit ctra thanh luOn dugc gifr 6 nhiet dQ bang khOng 86 qua su ffao Cdi ntriet qua mdt b0n, vdn tdc truydn nhigt ffong thanh bdng a
Ciu 3 X€t hinh trbn bdn kinh R c6 tam nam tai gOc toa d0 Gia srl (r, p) ld cdc toa d0 c{c, (r,il ld cdc toa dO pC Cac hai chidu Tim nghiOm cira phuong ffinh Laplace ddi vdi midn trong hinh trbn th6a mdn didu kiqn biOn Dirichlet:
u(r, p) l":" - u(R,p) : A + B sin29, trong d6 A vh s ld c6c hang sd
CAu 4 Cho b6n kinh vecto i_ ri+aV + rE, r: ld Hdy tfnh:
div [r.grad (r-')] , trong d6 n ld sd nguyOn
Ghi chit: Cdn bd coi thi kh1ng gidi thich gi th€m