Appendix 1
Ampère/Laplace Magnetic Actions Undergone by a Current Loop Placed in an External Magnetic Field
A1.1. Uniform magnetic field
In the case of a uniform field, the result of the Laplace forces is zero:
The torsor of the Laplace forces is therefore reduced to a torque whose moment is equal to 
The literal calculation of 
is somewhat heavier:
However, it can be shown that:
Moreover:
In a uniform field, the circuit orients itself until its magnetic moment is parallel to the field.
A1.2. Non-uniform magnetic field
In this question, it is considered that the spatial scale characteristic of the variations of B is large: B is only very weakly non-uniform. The goal is to calculate, in the expression of 
and the first non-zero term (in a limited development with respect to the fluctuating ...
Get Electromagnetism now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
