b) \( \begin{aligned} F_{R}=|q| E_{R} \\ F_{R}=1-1,6 \cdot 10^{-19} \mathrm{c} \mid 8,9 \mathrm{~N} / \mathrm{C} \\ F_{R}=1,6 \cdot 10^{-19} \mathrm{c} \cdot 8 ; 9 \mathrm{~N} / \mathrm{c}\end{aligned} \)
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Bonus Knowledge
When we talk about forces on charged particles in electric fields, it all connects back to the fundamental principles of electromagnetism formulated by the great minds like Coulomb and Faraday. The force \( F_{R} \) experienced by a charge in an electric field is directly proportional to the magnitude of the charge and the intensity of the field, emphasizing the elegance of nature's laws. Fun fact: the unit of charge, the coulomb, is named after Charles-Augustin de Coulomb, who laid down the groundwork for what we know today! In the real world, these concepts play a huge role in the design of everyday technologies. From the operation of mobile phones to the workings of electric vehicles, understanding the interactions of electric fields and charged particles allows engineers to optimize performance. For instance, the force calculations help in the design of capacitors and sensors, which rely on precise electrical interactions to function smoothly and efficiently!