Solution Found!
In Prob. 6.4, you calculated the force on a dipole by
Chapter 6, Problem 22P(choose chapter or problem)
Problem 22P
In Prob. 6.4, you calculated the force on a dipole by “brute force.” Here’s a more elegant approach. First write B(r) as a Taylor expansion about the center of the loop:
where r0 is the position of the dipole and ∇0 denotes differentiation with respect to r0. Put this into the Lorentz force law (Eq. 5.16) to obtain
Or, numbering the Cartesian coordinates from 1 to 3:
where δi j is the Kronecker delta (Prob. 3.52).
Questions & Answers
QUESTION:
Problem 22P
In Prob. 6.4, you calculated the force on a dipole by “brute force.” Here’s a more elegant approach. First write B(r) as a Taylor expansion about the center of the loop:
where r0 is the position of the dipole and ∇0 denotes differentiation with respect to r0. Put this into the Lorentz force law (Eq. 5.16) to obtain
Or, numbering the Cartesian coordinates from 1 to 3:
where δi j is the Kronecker delta (Prob. 3.52).
ANSWER:
Solution
Step 1 of 5
In this problem, we have already calculate the force on a dipole by brute force of by Taylor series expansion. Now we have to show that from Lorentz force law to obtain
