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Vector B is formed by the product of two gradients B = (∇u) × (∇v) ,...

Vector B is formed by the product of two gradients B = (∇u) × (∇v) , where u and v are scalar functions. Show that:

(a) B is solenoidal;

(b) A = 1/2(u∇v  − v∇u) is a vector potential for B, that is B =∇×A

Math   Calculus   
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