Question

Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es (x,y, z) by the transformat ion a) The line-element in Cartesian coordinates is given by d82-dr2+dy2+d22-De- termine the lne-elemen expressed in terms of the parabolic cylindrical coordinates b) Given F = 211,2) of the equation V22) F e where F depends only nu. Find the explicit form F-x F kF c) Solve the equation fro b) to find F Useful formulas: Given any ort hogonal eurvilinear coordinate (,2), with base unit vectors e, e, e Denote (x,,) the Cartesian coordinates, and e ey, e t he uni vectors of Cartesian coordination. Let r be the position vector 〔i.e. from origin to a point), and d8 be a line element vector field ▽ × v-hihhi | 옮 옳 옮 | where V = Viel + ½e2 + Vaes is a vector field. BQT Email ddess: bao. tawan,no

Answer 1

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