# Visuo-Haptic Simulations to Understand the Dependence of Electric Forces on Distance
## 1 Introduction  
Advances in multimodal interaction have enriched teaching-learning models. The theory of embodied cognition is based on the paradigm of adding senses, improving the learning experience, and allowing the student to acquire knowledge on a deeper and longer-term level [1]. Haptic technologies add the sense of touch in a virtual world, allowing users to perceive different sensations such as hardness, shape, weight, and texture of virtual objects in visuo-haptic simulators [2, 3]. Visuo-haptic learning environments allow the student's brain to receive stimuli from different channels, allowing a more complete experience and better acquisition of concepts and experience in the learning process [4]. Haptic devices recreate the sense of touch by computing interactions between the user and virtual objects, rendering force feedback on the user. Visuo-haptic environments that use low-cost haptics open up the possibility of using them both at home and ineducational spaces This technology has enabled the development and creation of novel interactive applications (Figure 1). Among other applications, visual technologies coupled with haptic devices have gained attention in Physics teaching due to their potential application to help understand the nature of different kinds of forces that appear in physical scenarios [5; 6; 7; 8; 9]. In particular, the usefulness of visuo-haptic implementations to sense those forces that cannot be tested manually have been explored, as the case for example of the electromagnetic forces, for which only indirect measures can be inferred from laboratory experiments. Several researches have been conducted with this purpose [10; 11; 12; 13; 14; 15]. In engineering education two of the basic key areas are Classical Mechanics and Electricity and Magnetism. In Classical Mechanics several visuo-haptic simulators have been proposed for better understanding the operation of simple machines [5; 13], gears [6], and the nature of friction forces [7; 8; 13; 16; 17], among other topics. Whereas Classical Mechanics deals mainly with tangible concepts, Electricity and Magnetism studies mostly abstract ones. For example, in the case of electrical forces between charge distributions, the student requires a lot of imagination to understand the essence of some interactions and the underlying physical concepts. It has been identified that undergraduate students often find Electricity and Magnetism ideas difficult and confusing [18]. Some of the main deficiencies are related to misconceptions of Maxwell's equations as well as misunderstandings between electric fields and their sources. Consequently, related problem-solving is troublesome [19]. Specifically, it has been reported that students have difficulty with electromagnetic induction, electric potential, and electric potential energy [20]. In this regard, the design and implementation of carefully designed visuo-haptic scenarios to help understand the nature of electromagnetic interactions can be suitable for the formation of engineering students. One important issue regarding the design of visuo-haptic simulators in Physics is the assessment of their impact on students' learning [6; 7]. Several studies suggest that statistically significant learning gains can be achieved when properly designed scenarios, combined with appropriate setups and guided experiments, are implemented [9; 15; 16]. Nevertheless, the need for further investigation to find optimal practices aimed to obtain improved student learning is still required. Therefore, the aim of this work is: (i) to present the design of three visuo-haptic simulators to study the nature of electric forces, (ii) to prove their implementation with engineering students, and (iii) to assess their impact on student learning and student perception. The layout of this paper is as follows. In Section 2, the related work is briefly outlined. In Section 3, the methodology followed in this research is presented. Section 4 is dedicated to data analysis and results. Section 5 includes a discussion of the main results.