Kemp, Grzegorczyk, and Kong Figure 4. Two particles centered at (a, y)=(100, 0),(300, 0)[nm are subject to the incident field pattern of Fig. 1. The integration paths for the Maxwell stress tensor applied to the two particles are shown by the dotted lines. The sum of the forces on the two individual articles obtained by the smaller two integration circles is equal to the force obtained by integrating over the large circular integration path (0,-300)m]isp=-01.4901018N/m. By taking the integration path surrounding both particles, the total force on the system composed of both particles is F= y20269. 10-9[N/ml which agrees with the sum of the individual forces. This example demonstrates that the divergence of the stress tensor gives the total force on all currents and charges enclosed by the integration path and hat the integration path needs not be concentric with the material For comparison with the stress tensor method, the Lorentz force is applied to bound electric currents in both particles. The distribution of force densities are shown in Fig. 5. Although the a -directed force integrates to zero for both particles due to symmetry, it can be seen that the local force densities vary throughout the particle. These forces act in compression or tension in the various regions of the particle. The total force on each particle is found by integration of the local force densities throughout the particles. The force for he particle at(a, y)=(0, 100)(nm] is F= y16500. 10-18(N/ml using 17, 534 integration points, and the total force on the particle at(x,y)=(0,-30{mm]isF=-91.4523·10-1N/m] using17,530 integration points, which is agreement with the results of the Maxwell stress tensor divergence834 Kemp, Grzegorczyk, and Kong p p b y x    Figure 4. Two particles centered at (x, y) = (100, 0), (−300, 0) [nm] are subject to the incident field pattern of Fig. 1. The integration paths for the Maxwell stress tensor applied to the two particles are shown by the dotted lines. The sum of the forces on the two individual particles obtained by the smaller two integration circles is equal to the force obtained by integrating over the large circular integration path. (x, y) = (0, −300) [nm] is F¯ = −yˆ1.4490 · 10−18 [N/m]. By taking the integration path surrounding both particles, the total force on the system composed of both particles is F¯ = ˆy2.0269 · 10−19 [N/m], which agrees with the sum of the individual forces. This example demonstrates that the divergence of the stress tensor gives the total force on all currents and charges enclosed by the integration path and that the integration path needs not be concentric with the material bodies. For comparison with the stress tensor method, the Lorentz force is applied to bound electric currents in both particles. The distribution of force densities are shown in Fig. 5. Although the ˆx-directed force integrates to zero for both particles due to symmetry, it can be seen that the local force densities vary throughout the particle. These forces act in compression or tension in the various regions of the particle. The total force on each particle is found by integration of the local force densities throughout the particles. The force for the particle at (x, y) = (0, 100) [nm] is F¯ = ˆy1.6500 · 10−18 [N/m] using 17, 534 integration points, and the total force on the particle at (x, y) = (0, −300) [nm] is F¯ = −yˆ1.4523 · 10−18 [N/m] using 17, 530 integration points, which is agreement with the results of the Maxwell stress tensor divergence