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Vectors in Spherical and Cylindrical

(a) Given A = a*p_hat + b*psi_hat + c*z_hat (cylindrical unit vectors), where a, b, and c are constants. Is A a constant vector (uniform vector field)? If not, find: the divergence and curl of A

(b) If A = a*r_hat + b*theta_hat + c*phi_hat in spherical coordinates, with constant coefficients. Is A a constant vector (uniform vector field)? If not, find: the divergence and the curl of A.

Solution Preview

Hello and thank you for the opportunity to help. Please note: All derivatives are partial derivatives even though they are denoted with 'd' and
d/dp (ap) is the same as

d (ap)
_____ = the partial derivative of a*p with respect to p.
dp

(a) In cylindrical coordinates,

divA = 1/p * [ d/dp (a*p) + d/dpsi ...

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