What is the difference between ((vec(B) * grad)vec(B))/(B) and grad * vec(B) ?

Emmy Swanson

Emmy Swanson

Answered question

2022-10-16

What is the difference between ( B ) B B and B ?
I was doing a vector calculus problem, and in the hint I got to introduced with the first term, and I wondered, what is the difference between these two expression?

Answer & Explanation

dippoliticsxu

dippoliticsxu

Beginner2022-10-17Added 9 answers

They are not the same. Notice that the divergence gives a number at each point (a scalar field) while the first expression in your answer is a vector. In fact, the j-th component of ( B ) B is
[ ( B ) B ] j = i = 1 B i B j x i ,
where x 1 = x x 2 = y and x 3 = z. . Your first expression just divides each of these components by a number (B), and therefore still results in a vector field.

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