Page 227 - Mechanics of Microelectromechanical Systems

214 Chapter 4
As a consequence, there is no force resultant acting on the loop, but there is a
couple produced by the two parallel and opposite forces of Fig. 4.33. The
moment of this couple is:

and its effect is to rotate the loop about the axis indicated in the same figure.

Figure 4.34 Circular loop carrying a current in an external magnetic field

A similar result can be obtained by using a circular loop of radius R, as
the one pictured in Fig. 4.34. The Lorentz force acting on a circular segment
of length dl, which is defined by an angle is:

and its magnitude is:

The total force acting on the circular loop can be found by summing up all
these elementary forces, which means calculating the following integral:

so, again, there is no resultant force acting on the loop. If one now considers
two elementary lengths that are situated at an angle disposed