FormulaHorizontal throw (throw distance, initial velocity, initial height) $$ w ~=~ v_0 \, \sqrt{ \frac{2\, y_0}{ g } } $$
FormulaHorizontal throw (throw duration, initial height) $$ t_{\text d} ~=~ \sqrt{ \frac{2\, y_0}{ g } } $$
FormulaBiot-Savart law for thin conductors (Magnetic field) $$ \boldsymbol{B}(\boldsymbol{r}) ~=~ \frac{\mu_0 \, I}{4\pi} \int_{S} \frac{\boldsymbol{r}-\boldsymbol{R}}{|\boldsymbol{r}-\boldsymbol{R}|^3} \times \text{d}\boldsymbol{s} $$
FormulaLong coil (magnetic field, number of turns, current) $$ \class{violet}{B} ~=~ \mu_0 \, \mu_{\text r} \, \frac{ \class{red}{I} \, N }{ l } $$
FormulaWave equation for B-field $$ \nabla^2 \, \boldsymbol{B} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \boldsymbol{B}}{\partial t^2} $$
FormulaWave equation for E-field $$ \nabla^2 \, \class{blue}{\boldsymbol{E}} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \class{blue}{\boldsymbol{E}}}{\partial t^2} $$
Formula3. Maxwell equation (integral form) $$ \oint_{L} \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ -\int_{A} \frac{\partial \class{violet}{\boldsymbol{B}} }{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$
Formula2. Maxwell equation (integral form) $$ \oint_A \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ 0 $$
Formula4. Maxwell equation (integral form) $$ \oint_{L} \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, \class{red}{I} ~+~ \int_{A} \frac{\partial \class{blue}{\boldsymbol{E}}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$
