\( \left. \begin{array} { l } { V = \int _ { R } ^ { + \infty } E d r } \\ { V = \frac { Q } { 4 \pi \varepsilon _ { 0 } } \lim _ { T \rightarrow \infty } \int _ { R } ^ { T } \frac { 1 } { r ^ { 2 } } d r } \\ { V = \frac { Q } { 4 \pi \varepsilon _ { 0 } } \lim _ { T \rightarrow + \infty } - \frac { 1 } { r } | _ { R } ^ { T } } \\ { V = \frac { Q } { 4 \pi \varepsilon _ { 0 } } \lim _ { T \rightarrow + \infty } ( - \frac { 1 } { T } - - \frac { 1 } { R } ) } \\ { V = \frac { Q } { 4 \pi \varepsilon _ { 0 } } \lim _ { T \rightarrow + \infty } ( - \frac { 1 } { T } + \frac { 1 } { R } ) } \\ { V = \frac { Q } { 4 \pi \varepsilon R } } \end{array} \right. \)

Did you know that the concept of electric potential originates from the work of pioneers like Charles-Augustin de Coulomb? In the late 18th century, he laid the foundation for electrostatics with his famous law of attraction and repulsion between charged particles. This was a time when scientists began to explore the invisible forces that govern interactions between charged bodies, ultimately leading to the formalization of potential energy and electric fields! In the real world, electric potential plays a crucial role in everything from designing electronic devices to understanding natural phenomena like lightning. For example, engineers rely on concepts of voltage to create safe and efficient electrical systems in homes and industries. Additionally, when you plug in your phone charger, you’re essentially harnessing electric potential to transfer energy from the outlet to your device, showcasing the practical application of those theoretical principles you just encountered!