# Solenoidal proof

1. Mar 1, 2012

### cristina89

Be f and g two differentiable scalar field. Proof that ($\nabla$f) x ($\nabla$g) is solenoidal.

2. Mar 1, 2012

### Dick

Show what you've done so far. What would you do to show a vector field is solenoidal?

3. Mar 1, 2012

### cristina89

Well, to be solenoidal, I know that $\nabla$ $\cdot$ ($\nabla$f x $\nabla$g) needs to be 0.

So,

$\nabla$ $\cdot$ ($\nabla$f x $\nabla$g) = $\nabla$g $\cdot$ ($\nabla$ x $\nabla$f) - $\nabla$f $\cdot$ ($\nabla$ x $\nabla$g)

Right? But why is this equal to zero?

4. Mar 1, 2012

### I like Serena

Last edited: Mar 1, 2012
5. Mar 2, 2012

### cristina89

Thank you so much!