Show that the following two vector ﬁelds are conservative and ﬁnd associated scalar potentials. (a) F...

Show that the following two vector ﬁelds are conservative and ﬁnd associated scalar potentials.
(a) F = 2ρsin(2φ) ρ + 2ρcos(2φ) φ + k
(b) F = (2r cos2 φ + sinθ cosφ) r + cosθ cosφ θ − [r(sin(2φ)/sinθ) + sinφ] φ

Expert Solution

Colby Messinger answered 1 year ago

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For each of the following vector fields F , decide whether it is conservative or not...

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(10x+7y)i+(7x+10y)jF(x,y)=(10x+7y)i+(7x+10y)j f(x,y)=f(x,y)= B. F(x,y)=5yi+6xjF(x,y)=5yi+6xj f(x,y)=f(x,y)= C. F(x,y,z)=5xi+6yj+kF(x,y,z)=5xi+6yj+k f(x,y,z)=f(x,y,z)= D. F(x,y)=(5siny)i+(14y+5xcosy)jF(x,y)=(5sin⁡y)i+(14y+5xcos⁡y)j f(x,y)=f(x,y)= E. F(x,y,z)=5x2i+7y2j+5z2k

For each of the following vector fields F , decide whether it is conservative or not...

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(−4x+5y)i+(5x+16y)j f(x,y)= ? B. F(x,y)=−2yi−1xj f(x,y)= ? C. F(x,y,z)=−2xi−1yj+k f(x,y,z)= ? D. F(x,y)=(−2siny)i+(10y−2xcosy)j f(x,y)= ? E. F(x,y,z)=−2x2i+5y2j+8z2k f(x,y,z)= ? Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

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Question

Show that the following two vector ﬁelds are conservative and ﬁnd associated scalar potentials. (a) F...

Solutions

Expert Solution

Related Solutions

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