Let F be a vector field in 3D and f a scalar function of three variables. Determ

Question

Let F be a vector field in 3D and f a scalar function of three variables. Determine whether the following are True or False. T F If Times F = 0 then_c F middot dr = 0 for any closed loop c. T F If the x- and y-components of F are 0 and S is a surface with sides parallel to the z-axis, then the flux of F through S is 0. T F If F = Times A and S is a closed surface, then the flux of F through S is 0. T F In order to find the integral of f around a closed loop c, one may apply Stokes' theorem to transform to a scalar surface integral. T F If S is a surface with normal N such that (Times F) middot N = 1 then the surface area of S can be computed as_partial differential S F middot dr.

Explanation / Answer

a) T , because net workdone in closed surface is always zero.
b) F
c) T , Because flux through the closed surface is 0
d) T

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