1. Let a vector field A take the following form in cylindrical coor...

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1. Let a vector field A take the following form in cylindrical coordinates: (a) Express the unit vectors r, and Z in Cartesian coordinates. Show your reasoning in your answer. [2] (b) Calculate the surface integral SA.ds, where S is the surface of a cylinder of outer radius R2 and inner radius R1 centred around the origin and extending from z = 0 to z = L. [3] (c) Calculate B =VxA. [3] (d) Show that the surface integral B d S = 0, where S is the surface of the same cylinder. [2] 2. A time-varying scalar field is given by (a) Calculate atV. [2] (b) Let x and y have the following time dependence: x(t)=at+b and ((t) and z(t) = d, with a, b, and d constants. Calculate dV C dt [3]

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