Question

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.

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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 the origin? Find all functions f(s), differentiable for s0, such that f(s)r is solenoidal everywhere except at the origin in 3-space div (s3r) - 3s(x2 + y + z2)3s36s3(Type the answer as an expression involving the variable s.) The vector field s"r is solenoidal, provided k -3 Thevectorfield fsrís solen idalfor allfunctions oftheformGs) = cDiwherec The vector field f s r is so eno dal for all functions of the form fis = C where C is an arbitrary constant, and only functions of this form.

Answer 1

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div (.fcs).wj = Kfs) (¥4(s))叩 十 (4)f(s)