Question

Find whether the vector is solenoidal, E = yz i + xz j + xy k

(a) Yes, solenoidal

(b) No, non-solenoidal

(c) Solenoidal with negative divergence

(d) Variable divergence

The question was posed to me by my school teacher while I was bunking the class.

This key question is from Divergence topic in portion Vector Calculus of Electromagnetic Theory

Answer 1

Correct option is (a) Yes, solenoidal

To explain I would say: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.