Problem 3.48 Determine if each of the following vector fields is solenoidal. conservative, or both: (c)...
Only the Matlab part !!! Question 2 For the following vector fields F determine whether or not they are conservative. For the conservative vector fields, construct a potential field f (i.e. a scalar field f with Vf - F) (a) F(z, y)(ryy,) (b) F(z, y)-(e-y, y-z) (c) F(r, y,z) (ry.y -2, 22-) (d) F(x, y, z)=(-, sin(zz),2, y-rsin(x:) Provide both your "by hand" calculations alongside the MATLAB output to show your tests for the whether they are conservative, and to...
7. Determine whether the following vector fields are conservative. If they are, then find a potential function (b) F:cos(),2y, -sin)> 7. Determine whether the following vector fields are conservative. If they are, then find a potential function (b) F:cos(),2y, -sin)>
Determine if the following vector fields F: 2 CR" + R" are conservative. In case they are conservative, find a potential function f, that is, such that F= Vf. a) F(1, y) = (x²y, zy), N=R? b) F(1, y, z) = (ze", 22 sin(z), 2+z+1), N=R3 c) F(x,y) = (e cosy, -efsiny), R=R2
CALCULUS; The vector field f(s)r is solenoidal for all functions of the form f(s) = C .... where C is an arbitrary constant, and only functions of this form. Please provide a detailed answer. Thanks. Let xi+ yj + zk be the position vector of a general point in 3-space and let s Irl be the length of r. Calculate the divergence of s3r. For what value of the constant k is the vector field s r solenoidal except at...
Problem 7. Given that each of the following vector fields F is conservative Find a potential function f such that f = F and evaluate fe F dr along the given curve C 1. F(r,y) y C: F(t)(t3- 2t, t3 + 2t), 0 <t<1 2. F(x,y, ) yze"* i + e#* j + xye k C: F(t)(t2 1)i +(2 -1)( -2t)k, 0t 2
1. One of the two vector fields listed below is conservative. The other one is not conservative. (a) Determine which one of these fields is conservative. Label the conservative field F and and find a potential function f for it. Label the other field G and prove that G is NOT conservative. (b) Use the fundamental theorem of line integrals to compute SCF . dr, where C is the curve parameterized by (c) Compute Jc G-dr, where C is the...
(1 point) 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, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (-140 – 4y) i + (-4x + 12y)j f (x, y) = B. F (x, y) = -7yi - 6xj f(x,y) = C. F (2, y) =...
(1 point) 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, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F(x, y) = (-14x + 4y)i + (4x + 2y)j f (x, y) = B. F(x, y) = -7yi – 6xj f (x, y) = C. F(x, y) = (-7 sin...
we need to determine if the vector field depicted in graph 1 and graph 2 are conservative by using the last 3 bullets points in the picture Project 1. Fundamental theorem of line integrals In our course we learned the fundamental theorem of line integrals: if F is a conservative vector field with potential f and C is a curve connecting point A to b, then f-dr = f(B)-f(A). Moreover it happens if and only if for any closed curve...
1. Find the divergence, curl and Laplacian of the following vector fields (a) E = psin o Ô-p?Ộ - zk, where p, 0, z are cylindrical coordinates. (b) F = sin O † – rsin e ôn, where r, 0, $ are spherical coordinates.