Question

Prove that the vector A = 3yz2 i + 4x322 j - 3x2y2 k is solenoidal

Answer 1

A is solenoidal if $\nabla . A = 0$

$\nabla. A = \frac{\partial(3yz^2)}{\partial x} + \frac{\partial(4x^3z^2)}{\partial y} - \frac{\partial(3x^2y^2)}{\partial z} = 0+0-0 = 0$

as desired.