Forces and stresses in an electromagnetic field

IN MANY engineering problems, it is required to calculate the forces on dielectric and magnetic materials when they are placed in an electromagnetic field. Quite often, it is also desirable to know the force density (the distribution of the forces over the entire volume and the surface) of the material. Methods of calculating the forces and the force densities are given in many books on electromagnetic theory. The treatment of the problem generally leads the reader to believe that the solution to the problem is known and that the equations given are correct. However, if one investigates the equations given in different literatures, one finds that they differ considerably and they give completely different force densities. The author failed to find in the literature a single paper which discusses all the different methods and which points out the most important differences among the theories. The author also found that the differences among the theories are generally not well known to engineers. It is for this reason that this paper is written. Typical questions discussed are as follows: 1. How do the forces originate? 2. Where are they located? 3. Is there any shear force acting on the material? 4. After a ferromagnetic material is saturated, is there any further increase in force as a result of an increase in the field intensity?