P19-040 – Principle of Superposition

\boxed{\overrightarrow{E}_{net}=\overrightarrow{E}_{1}+\overrightarrow{E}_{2}+\overrightarrow{E}_{3}+\dots}

\boxed{{\overrightarrow{E}}_{net}={\overrightarrow{E}}_1+{\overrightarrow{E}}_2}

\begin{aligned}
{\overrightarrow{E}}_{net}={\overrightarrow{E}}_1+{\overrightarrow{E}}_2\ \ \ \ &\Rightarrow \ \ \ \ \ \left\{ \begin{array}{c}
E_{net\ x}=E_{1x}+E_{2x} \\ 
E_{net\ y}=E_{1y}+E_{2y} \end{array}
\right. \\
\\
&\Rightarrow \ \ \ \ \ \left\{ \begin{array}{c}
E_{net\ x}=E_1{\mathrm{cos} \left({\theta }_1\right)\ }+E_2{\mathrm{cos} \left({\theta }_2\right)\ } \\ 
E_{net\ y}=E_1{\mathrm{sin} \left({\theta }_1\right)\ }-E_2{\mathrm{sin} \left({\theta }_2\right)\ } \end{array}
\right.
\end{aligned}

E_{net}=\sqrt{E^2_{net\ x}+E^2_{net\ y}}=\sqrt{{\left(E_1{\mathrm{cos} \left({\theta }_1\right)\ }+E_2{\mathrm{cos} \left({\theta }_2\right)\ }\right)}^2+{\left(E_1{\mathrm{sin} \left({\theta }_1\right)\ }-E_2{\mathrm{sin} \left({\theta }_2\right)\ }\right)}^2}