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.
(b) Calculate the surface integral
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.
(c) Calculate B =VxA.
(d) Show that the surface integral
B d S = 0,
where S is the surface of the same cylinder.
2. A time-varying scalar field is given by
(a) Calculate atV.
(b) Let x and y have the following time dependence:
z(t) = d,
with a, b, and d constants. Calculate dV
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