## The 4 Maxwell's Equations: Important Basics You Need to Know

Simple explanation of the Maxwell's equations for beginners. The divergence integral and the curl integral theorems are also explained.

Maxwell equations and electromagnetic waves

Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

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Lesson ## The 4 Maxwell's Equations: Important Basics You Need to Know

Simple explanation of the Maxwell's equations for beginners. The divergence integral and the curl integral theorems are also explained.

Video ## Maxwells Equations explained extensively in 40 minutes!

The Maxwell’s equations are studied in the second semester of physics. Here you will learn EVERYTHING about them just within 40 minutes - explained for BEGINNERS!

## Related formulas

Formula ## 1. Maxwell equation in integral form (E-field, charge)

`$$ \oint_A \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ \frac{\class{red}{Q}}{\varepsilon_0} $$`Formula ## 1. Maxwell equation (differential form)

`$$ \nabla ~\cdot~ \class{blue}{\boldsymbol{E}} ~=~ \frac{\class{red}{\rho}}{\varepsilon_0} $$`Formula ## 2. Maxwell equation (differential form)

`$$ \nabla \cdot \class{violet}{\boldsymbol{B}} ~=~ 0 $$`Formula ## 2. Maxwell equation (integral form)

`$$ \oint_A \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{a} ~=~ 0 $$`Formula ## 3. Maxwell equation (differential form)

`$$ \nabla \times \class{blue}{\boldsymbol{E}} ~=~ -\frac{\partial \class{violet}{\boldsymbol{B}}}{\partial t} $$`Formula ## 3. Maxwell equation (integral form)

`$$ \oint_{L} \class{blue}{\boldsymbol{E}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ -\int_{A} \frac{\partial \class{violet}{\boldsymbol{B}} }{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$`Formula ## 4. Maxwell equation (integral form)

`$$ \oint_{L} \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, \class{red}{I} ~+~ \int_{A} \frac{\partial \class{blue}{\boldsymbol{E}}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a} $$` - 2
Lesson ## 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.

## Related formulas

Formula ## Wave equation for E-field

`$$ \nabla^2 \, \class{blue}{\boldsymbol{E}} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \class{blue}{\boldsymbol{E}}}{\partial t^2} $$`Formula ## Wave equation for B-field

`$$ \nabla^2 \, \boldsymbol{B} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 \boldsymbol{B}}{\partial t^2} $$`

` $$ \boldsymbol{B}(\boldsymbol{r}) ~=~ \frac{\mu_0 \, I}{4\pi} \int_{S} \frac{\boldsymbol{r}-\boldsymbol{R}}{|\boldsymbol{r}-\boldsymbol{R}|^3} \times \text{d}\boldsymbol{s} $$ `