Vector Calculus Problem - Griffith Textbook

[Bruce Dawk]

I have a problem in the Griffith textbook (Introduction to Electrodynamics), Question 1.21, where it asks what is the meaning of the vector (A.∇)B, my simplistic approach would be to calculate the divergence of A which should be a scalar and multiply it out by Bx,By,Bz) to compute the x component of the expression. However in the solution manual (available by searching Introduction to Electrodynamics Solutions and clicking on the Scribd link) it seems to be the other way around.

I just don't understand why this is, can someone clarify please?

 

[jedishrfu]

I think this is the directional derivative. It gives the change of a field B in the direction A.

See wikipedia for details:

http://en.wikipedia.org/wiki/Del

 

[lurflurf]

(A.∇)B and B(∇.A) are not equal because that operator acts to the right so in
(A.∇)B
B is differentiated while in
B(∇.A)
A is differentiated

 

[Bruce Dawk]

Thanks all. Its quite clear now.