Formula: Electric Potential and Potential Energy Electric charge
$$W_{\text{pot}} ~=~ \class{red}{q} \, V_{\text{e}}$$
$$W_{\text{pot}} ~=~ \class{red}{q} \, V_{\text{e}}$$
$$V_{\text{e}} ~=~ \frac{ W_{\text{pot}} }{ \class{red}{q} }$$
$$\class{red}{q} ~=~ \frac{ W_{\text{pot}} }{ V_{\text{e}} }$$
Potential energy
$$ W_{\text{pot}} $$ Unit $$ \mathrm{J} = \mathrm{Nm} = \frac{ \mathrm{kg} \, \mathrm{m^2} }{ \mathrm{s}^2 } $$
Potential energy of a test charge \(\class{red}{q}\) in an electric potential field generated by a source charge \(\class{red}{Q}\).
Electric potential
$$ V_{\text{e}} $$ Unit $$ \frac{\mathrm{J}}{\mathrm{C}} $$
Electric potential at a distance from a charge \( \class{red}{Q} \) which generates this potential. The potential indicates the electric potential energy that a test charge gains or must dissipate when placed from an infinite distance to a distance \( r \) from the source charge.
Test charge
$$ \class{red}{q} $$ Unit $$ \mathrm{C} = \mathrm{As} $$
Test charge placed in the electric potential of a source charge.