# Visuo-Haptic Simulations to Understand the Dependence of Electric Forces on Distance
## 6 Conclusions and Future Work  
From the results presented in the previous sections, several conclusions can be obtained. Three visuo-haptic simulators were carefully designed to recognize the dependence on distance of the electric force between different electric charge distributions: point charge, line charge, and plane charge. Engineering students of EM and EF courses practiced with the simulators. Pre-test and post-tests were applied before and after students used the simulators and average absolute and relative learning gains were calculated. \(t\)-tests showed that the learning gains were statistically significant. All students in the entire sample had the correct answers for questions regarding the attractive or repulsive nature of the electric force between charges with different or the same signs. This result is explained by the fact that this is a basic concept first taught in introductory Physics high school courses and also at the beginning of the engineering EM and EF courses, therefore the use of the visuo-haptic simulator did not produce any learning gain. From the results of this study, it can be concluded that experiment using the visuo-haptic simulator did not help students to better perceive the inverse square dependence of the electric force between point charges. This also can be due to the fact that students already obtained a high average grade in the pre-test; therefore, there was a rather small interval for improvement. On the other hand, it is inferred that the experiment with the visuo-haptic simulator strongly improved the student recognition of the correct distance dependence law for the line distribution (\(1/r\)) and the no-dependence on distance for the plane charge distribution. In particular, for the plane charge, the relative gain resulted very high. This finding encourages authors to develop additional simulators for related topics as other electric charge distributions and magnetic forces. The more advanced students of the EF section already obtained high grades in the pre-test, therefore their average learning gains were not statistically significant except for the case of the plane charge, where remarkably all of them obtained the right answer in the post-test. This result suggests that in general, the impact of the visuo-haptic simulators proposed in this research is higher for students with lower familiarity with electric forces, and therefore they may have an important potential with high school or even middle school students in introducing them to understand the distance dependence of the electric forces for different charge distributions. For the more advanced students, more complex visuo-haptic scenarios may be developed, as probing more sophisticated charge distributions and/or simulators to test magnetic forces on wires and solenoids. This remains as future work. The learning gains obtained in the present work give support to the hypothesis that the integration of an appropriate 3D visualization with suitable experiment design and a suitable guide of activities may help to promote significant student learning on the behavior of electric forces in the vicinity of a given charge distribution. As additional future work, the authors foresee the design of other simulators for electricity and magnetism forces, as well as for other physics areas. At the same time, authors strongly suggest implementing the use of visuo-haptic simulators since middle or high schools to introduce students to the study of electric and magnetic interactions. Regarding the improvement of our visuo-haptic simulators, some extensions can be added in the future. The incorporation of electric field lines and equipotential surfaces to the visual interfaces of the visuo-haptic simulators to obtain an enhanced perception and understanding of the electric forces and fields around the charge distributions is highly recommended. Students could move the test charges parallel or perpendicular to the filed lines or equipotential surfaces and assess the corresponding changes in the electric force intensity.