force parallel to the th axis suffered by a surface normal to the th axis per unit of area. Indeed, the diagonal elements give the tension (pulling) acting on a differential area element normal to the corresponding axis. Unlike forces due to the pressure of an ideal gas, an area element in the electromagnetic field also feels a force in a direction that is not normal to the element. This shear is given by the off-diagonal elements of the stress tensor. The Maxwell stress tensor is a complex number whose real part is the Poynting momentum flux density. In magnetostatics If the field is only magnetic (which is largely true in motors, for instance), some of the terms drop out, and the equation in SI units becomes: For cylindrical objects, such as the rotor of a motor, this is further simplified to: where is the shear in the radial (outward from the cylinder) direction, and is the shear in the tangential (around the cylinder) direction. It is the tangential force which spins the motor. is the flux density in the radial direction, and is the flux density in the tangential direction. In electrostatics In electrostatics the effects of magnetism are not present. In this case the magnetic field vanishes, i.e. , and we obtain the electrostatic Maxwell stress tensor. It is given in component form by and in symbolic form by where is the appropriate identity tensor usually . Eigenvalue The eigenvalues of the Maxwell stress tensor are given by: These eigenvalues are obtained by iteratively applying the Matrix Determinant Lemma, in conjunction with the Sherman–Morrison formula. Noting that the characteristic equation matrix, , can be written as where we set Applying the Matrix Determinant Lemma once, this gives us Applying it again yields, From the last multiplicand on the RHS, we immediately see that is one of the eigenvalues. To find the inverse of , we use the Sherman-Morrison formula: Factoring out a term in the determinant, we are left with finding the zeros of the rational function: Thus, once we solve we obtain the other two eigenvalues. See also Ricci calculus Energy density of electric and magnetic fields Poynting vector Electromagnetic stress–energy tensor Magnetic pressure Magnetic tension force References David J. Griffiths, "Introduction to Electrodynamics" pp. 351–352, Benjamin Cummings Inc., 2008 John David Jackson, "Classical Electrodynamics, 3rd Ed.", John Wiley & Sons, Inc., 1999. Richard Becker, "Electromagnetic Fields