Course Fundamentals of electrodynamics
Maxwell equations and electromagnetic waves
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
- 1
Related formulas
Formula $$ \oint_A \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ \frac{\class{red}{Q}}{\varepsilon_0} $$1. Maxwell equation in integral form (E-field, charge)
Formula $$ \nabla ~\cdot~ \class{blue}{\boldsymbol{E}} ~=~ \frac{\class{red}{\rho}}{\varepsilon_0} $$1. Maxwell equation (differential form)
Formula $$ \nabla \cdot \class{violet}{\boldsymbol{B}} ~=~ 0 $$2. Maxwell equation (differential form)
Formula $$ \oint_A \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ 0 $$2. Maxwell equation (integral form)
Formula $$ \nabla \times \class{blue}{\boldsymbol{E}} ~=~ -\frac{\partial \class{violet}{\boldsymbol{B}}}{\partial t} $$3. Maxwell equation (differential form)
Formula $$ \oint_{L} \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ -\int_{A} \frac{\partial \class{violet}{\boldsymbol{B}} }{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$3. Maxwell equation (integral form)
Formula $$ \oint_{L} \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, \class{red}{I} ~+~ \int_{A} \frac{\partial \class{blue}{\boldsymbol{E}}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$4. Maxwell equation (integral form)
- 2
Related formulas
Formula $$ \nabla^2 \, \class{blue}{\boldsymbol{E}} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \class{blue}{\boldsymbol{E}}}{\partial t^2} $$Wave equation for E-field
Formula $$ \nabla^2 \, \boldsymbol{B} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \boldsymbol{B}}{\partial t^2} $$Wave equation for B-field
Related Illustrations
