indrice Coordinetes Prove that in cylindred coordinates carte sian Coordinates,
ID: 1405387 • Letter: I
Question
indrice Coordinetes Prove that in cylindred coordinates carte sian Coordinates, -start with the expresion pr and uce andetween tu coresponding unit Vectors cme ,z ) and ci, relhons bekueen th Cortesian aud eyiadnicd coondats the i) cyindrica Find the fer the Jivejene avecter F in ylindricaut ex pression tmemn ( Volume element . Calculut the net F1ixout u'ng +de Yes u :@ por Vq Find vip i^ cylindri cal coordinat.a using tite result in por V4 F Find th-3 componta-f o'sF in cylindn'ad coordinates using stoker theeren,0r (VKf) ,comput Ovnd1 F.de amul the l.PL and bounded by the Coordine,e+dej2+Ztdz the line inte rt .de around the loopLí. an bound by t coordExplanation / Answer
Sorry We are not allowed to answer more than one question at a time , so I am answering first one.
So we have to calcualte gradient, I am using P instead of del operator
So P(phi) = (d(phi)/dr)dr + (d(phi)/d(theta))dtheta + (d(phi)/dz)dz
here d means curl
We also define
Pu = Pu.dr
(d(phi)/dr)dr + (d(phi)/d(theta))dtheta + (d(phi)/dz)dz = (Pu)phi d(r) + (Pu)theta (r)d(theta) + (Pu)z dz
(Pu)phi = d(u)/d(r)
(Pu)theta = (1/r)d(u)/d(theta)
(Pu)z = du/dz
P(Phi) = rd(Phi)/dr + theta(d(theta)/d(theta)) + z(d(Phi)/dz)
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