Question

If A and B are irrotational, then A×B is *


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Answer 1

Answer:

Ok

Explanation:

I have given here:

Curl(A→)=0→ and Curl(B→)=0→

So, to prove solenoidal the divergence must be zero i.e.:

=∇⋅(E→×H→)

Where do I go from here? I came across scalar triple product which may be applied here in some way I suppose if ∇ is a vector quantity.

Ok hope it helps you

Answer 2

Answer:

By problem ∇ × A = 0 and ∇ × B = 0,

it follows that B .(∇ × A) = 0

A. (∇ × B) = 0 Subtracting,

B .(∇ × A) − A.(∇ × B) = 0

Now ∇ .(A × B) = B .(∇ × A) − A.(∇ × B)

Therefore ∇ .(A × B) = 0,

so that (A × B) is solenoidal