Solution Found!
The vector potential for a uniform magnetostatic field is
Chapter 10, Problem 8P(choose chapter or problem)
Problem 8P
The vector potential for a uniform magnetostatic field is (r×B) (Prob. 5.25). Show that in this case, and confirm that Eq. 10.20 yields the correct equation of motion.
Reference equation 10.20
Reference prob 5.25
If B is uniform, show that works. That is, check that ∇ · A = 0 and ∇ × A = B. Is this result unique, or are there other functions with the same divergence and curl?
Questions & Answers
QUESTION:
Problem 8P
The vector potential for a uniform magnetostatic field is (r×B) (Prob. 5.25). Show that in this case, and confirm that Eq. 10.20 yields the correct equation of motion.
Reference equation 10.20
Reference prob 5.25
If B is uniform, show that works. That is, check that ∇ · A = 0 and ∇ × A = B. Is this result unique, or are there other functions with the same divergence and curl?
ANSWER:
Solution 8P
Step 1 of 3:
The vector potential of a uniform magnetic field is, we need to prove that .
Given,
So,
Implies,
And,
So,
