\(\def \u#1{\,\mathrm{#1}}\)
\(\def \abs#1{\left|#1\right|}\)
\(\def \ast{*}\)
\(\def \deg{^{\circ}}\)
\(\def \tau{\uptau}\)
\(\def \ten#1{\times 10^{#1}}\)
\(\def \redcancel#1{{\color{red}\cancel{#1}}}\)
\(\def \BLUE#1{{\color{blue} #1}}\)
\(\def \RED#1{{\color{red} #1}}\)
\(\def \PURPLE#1{{\color{purple} #1}}\)
\(\def \th#1,#2{#1,\!#2}\)
\(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\)
\(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\)
\(\def \dotspot{{\color{lightgray}{\circ}}}\)
\(\def \ccw{\circlearrowleft}\)
\(\def \cw{\circlearrowright}\)

How Things Move

Why Things Move

electric potential energy

Absent any other forces, charges will always spontaneously move in the direction that decreases their potential energy as quickly as possible.

equipotential line

\(PE_T=q_TV\)

capacitance

farads

- capacitance (\(C\))
*measured in* Farads \(C={Q\over \Delta V}\)