Vector Calculus Problem - Griffith Textbook

In summary, there is a question regarding the meaning of the vector (A.∇)B in the Griffith textbook (Introduction to Electrodynamics), Question 1.21. The suggested approach is to calculate the divergence of A and multiply it by Bx, By, and Bz to find the x component. However, the solution manual seems to use the opposite approach. It is clarified that this is the directional derivative, which gives the change of a field B in the direction A. It is also noted that (A.∇)B and B(∇.A) are not equal because the operator acts to the right.
  • #1
Bruce Dawk
3
0
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?
 
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  • #3
(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
 
  • #4
Thanks all. Its quite clear now.
 

1. What is vector calculus?

Vector calculus is a branch of mathematics that deals with the differentiation and integration of vector fields, which are functions that assign a vector to each point in space.

2. What is a vector field?

A vector field is a function that assigns a vector to each point in space. It can represent physical quantities such as velocity, force, or electric and magnetic fields.

3. Why is vector calculus important?

Vector calculus is important in many fields, including physics, engineering, and computer graphics. It provides a powerful tool for analyzing and solving problems involving vector quantities.

4. What is the difference between a scalar and a vector?

A scalar is a single quantity that only has magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature and mass, while examples of vectors include velocity and force.

5. What are some common applications of vector calculus?

Vector calculus has many applications, such as in physics for analyzing motion and forces, in engineering for designing structures and systems, and in computer graphics for creating visual effects and animations. It is also used in many other fields, including economics, biology, and statistics.

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