For each of the following vector fields F , decide whether it is conservative or
ID: 1887237 • Letter: F
Question
For each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, ?f=F). If it is not conservative, type N.A. F(x,y)=(?16x+8y)i+(8x+2y)j
f(x,y)=
B. F(x,y)=?8yi?7xj
f(x,y)=
C. F(x,y,z)=?8xi?7yj+k
f(x,y,z)=
D. F(x,y)=(?8siny)i+(16y?8xcosy)j
f(x,y)=
E. F(x,y,z)=?8x2i+8y2j+1z2k
f(x,y,z)=
Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
Explanation / Answer
The requirement for a field to be conservative field is that the curl of the field vanishes: ?xF = 0 i............j............k ?/?x......?/?y........?/?z Fx........Fy..........Fz ?xF = i(?Fz/?y - ?Fy/?z) + j(?Fz/?x - ?Fx/?z) + k(?Fy/?x - ?Fx/?y) = 0 ?xF = i(0 - 0) + j(0 - 0) + k[?(-x+6y)/?x - ?(-4x-y)/?y ?xF = k(-1 + 1) = 0 Thus, F(x,y) is a conservative field. put values and get answer
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