Electromagnetic wave (EM wave) LessonLevel 3 (with higher mathematics)Electromagnetic wave and its E-field and B-field components Here you will learnthe wave equations for the E-field and B-field of an electromagnetic wave and how it can be simplified to a plane wave.
Current + time-dependent E-field generate a rotating B-field and vice versa Formula4th Maxwell Equation in Integral Form $$ \oint_{L} \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, \class{red}{I} ~+~ \int_{A} \frac{\partial \class{blue}{\boldsymbol{E}}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$
Time changing magnetic field generates a rotating electric field and vice versa Formula3. Maxwell equation (differential form) $$ \nabla \times \class{blue}{\boldsymbol{E}} ~=~ -\frac{\partial \class{violet}{\boldsymbol{B}}}{\partial t} $$
Time changing magnetic field generates a rotating electric field and vice versa Formula3. Maxwell equation (integral form) $$ \oint_{L} \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ -\int_{A} \frac{\partial \class{violet}{\boldsymbol{B}} }{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$
Second Maxwell equation in integral form Formula2. Maxwell equation (differential form) $$ \nabla \cdot \class{violet}{\boldsymbol{B}} ~=~ 0 $$
Second Maxwell equation in integral form Formula2. Maxwell equation (integral form) $$ \oint_A \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ 0 $$
Positive charge - electric field lines Formula1. Maxwell Equation (Differential Form) $$ \nabla ~\cdot~ \class{blue}{\boldsymbol{E}} ~=~ \frac{\class{red}{\rho}}{\varepsilon_0} $$
AC circuit with a capacitive reactance of the capacitor FormulaCapacitive Reactance (Capacitance, Frequency) $$ X_{\text C} ~=~ -\frac{1}{2\pi \, f \, C} $$
Ohm's law - linear relationship between current and voltage FormulaOhm's Law (Resistance, Voltage, Current) $$ U ~=~ R \, I $$
Electric current between plus and minus pole FormulaElectric current (definition) $$ I ~=~ \frac{Q}{t} $$
Plate capacitor FormulaPlate Capacitor (Energy, Electric Field) $$ W_{\text{e}} ~=~ \frac{1}{2} \, \varepsilon_0 \, \varepsilon_{\text r} \, V \, E^2 $$
Electric force on a charge in a plate capacitor FormulaPlate Capacitor (Force, Voltage, Charge, Distance) $$ F ~=~ q \, \frac{U}{d} $$
RLC series circuit of resistor (R), coil (L) and capacitor (C) FormulaResonant RLC Series Circuit (Maximum Current, Voltage, Total Impedance) $$ I_0 ~=~ \frac{ U_0 }{ \sqrt{ R^2 ~+~ \left( \omega \, L ~-~ \frac{1}{\omega \, C} \right)^2 } } $$