Calculating Curl of F and Potential for various n values
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Please help with the following information.
a) Calculate the curl of F=r^n*(xi+yj)
b) For each n for which curlF=0 , find a potential g such that F=grad(g). (Hint: look for a potential of the form g=g(r), with r=sqrt(x^2+y^2). Watch out for a certain negative value of n which the formula is different.)
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Solution Summary
The following post helps with calculus problems. The first problem calculates the curl of F and the second calculates the potential for all values n with special attention to n =-2.
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a) calculate the curl of F=r^n*(xi+yj)
F = Mi + Nj;
M = r^n*x ; N = r^n*y
r = sqrt(x^2 + y^2)
Find Nx, partial of N w.r.t. x and My, partial of M w.r.t. y
Nx = y*(n/2)*(x^2 + y^2)^[(n/2)-1]* (2y) = n*x*y*(x^2 + y^2)^[(n/2)-1]
My = x*(n/2)*(x^2 + y^2)^[(n/2)-1]* (2x) = n*x*y*(x^2 + y^2)^[(n/2)-1]
Curl F = (Nx - My) k = 0
b) For each n for which curlF=0 , find a potential g such that F=grad(g). (Hint: look for a potential of the form g=g(r), with r=sqrt(x^2+y^2). Watch out for a ...
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