Confusion in the derivation of the force on a magnetic dipole

[timetraveller123]

wait i was looking through wikipedia and found this

this seems to suggest
$(A \cdot \nabla)B$
is not
$A \cdot (\nabla B)$

 

[TSny]

wait i was looking through wikipedia and found this

this seems to suggest
$(A \cdot \nabla)B$
is not
$A \cdot (\nabla B)$

Here, the notation $\nabla B$ is not the dyadic formed from $\nabla$ and $B$. So, here,

$A \cdot (\nabla B) \neq (A \cdot \nabla)B$.

Here, $\nabla B$ is the gradient of the vector B as define at https://en.wikipedia.org/wiki/Gradient#Gradient_of_a_vector
or in (1.14.3) here http://homepages.engineering.auckla...ensors/Vectors_Tensors_14_Tensor_Calculus.pdf

In matrix notation, the gradient of B, $\nabla B$, as used in the Wikipedia article is the transpose of the matrix representing the dyadic $\left( \nabla B \right)_{\rm dyadic}$.

See also the thread https://www.physicsforums.com/threads/gradients-of-vectors-and-dyadic-products.139000/​

 

[timetraveller123]

ok thanks again i will look more into the subject