Introducing the virtual air gap scheme to the Kelvin force densities with external and total field

Here, to calculate the electromagnetic body force density and total force the expression for Kelvin force density was expanded by incorporating the virtual air gap scheme. Conventionally, this Kelvin force density can be utilized by using external applied field and total field acting on a dipole. Since there is no well-accepted manipulating technique, it has been difficult to directly compute the Kelvin force by adopting the external field approach; however, using the virtual air gap scheme, the direct calculation of both Kelvin force density with external applied field and the Kelvin force density expression with total field as the local distributions of body force density was able to be evaluated. Numerical results showed the validity of our proposed method.