# Visuo-Haptic Simulations to Understand the Dependence of Electric Forces on Distance
## 2 Related Work
Recent visuo-haptic simulators for Electricity and Magnetism have concentrated on helping students to determine the direction of the electric/magnetic forces to infer the corresponding geometry of electric/magnetic fields. [PERSON] and [PERSON] presented a game scenario in which the student can move a charged particle through an electromagnetic field to _feel_ the Lorentz force exerted on it in order to test the direction of the vector-cross product between the charge velocity and the magnetic field [15]. The results of this research suggest that the appropriate design of visual-haptic interfaces to present abstract concepts promotes a greater commitment among students and therefore greater learning can be achieved. In this regard, [PERSON] et al. [13] and [PERSON] et al. [27] have performed preliminary studies of the understanding of the dependence of the electric force with distance for three charge distributions: point charge, line charge, and plane charge, which have \(1/r^{2}\), \(1/r\) and constant distance dependencies,respectively. Students were able to test with the haptic device the force strength at different distances from each of these charge distributions, and these authors reported an interesting trend of increasing students' learning gains on their recognition of the distance dependence through the comparison of post and pre-test grades. Nevertheless, they also pointed out that their findings were still not statistically significant and that future studies with larger student samples should be performed to further assess the impact of the simulators on increasing student learning. Given the fact that typical electricity and magnetism graphical displays of the visuo-haptic simulators presented in the literature are usually displayed in two dimensions, it has also been suggested the design of appropriate 3D graphical displays for these simulators to improve the depth perception, which is important to recognize the spatial behavior of the electromagnetic forces and to better engage students [13; 14; 15]. Therefore, considering the previous arguments and continuing the work described in [13; 27], a new study of the distance dependence of the electric force produced by different charge distributions is presented. The main purpose is that students perceive and quantify the behavior of the electric force with distance for these charge distributions. The proposed visuo-haptic simulators incorporate (i) a novel 3D graphical display for the visuo-haptic simulators aimed to better perceive the 3D dimension (depth), where the student can adjust the viewing perspective, and (ii) a larger student sample compared to those included in the preliminary works. Therefore, in this research, three visuo-haptic simulators for the sake of understanding the nature of electric forces produced by different charge distributions were implemented: (a) point charge, (b) line charge, and (c) plane charge. In particular, we were interested in exploring whether the simulators can help students to distinguish the dependence on distance of the electric forces exerted by each charge distribution on a point charge.