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Illustration Electric flux and enclosed charge (1st Maxwell equation)

Erste Maxwell-Gleichung (Gauß-Gesetz als Integralform)
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The first Maxwell equation in integral form:\[ \oint_A \boldsymbol{E} ~\cdot \text{d}\boldsymbol{a} ~=~ \frac{Q}{\varepsilon_0} \]connects the charge \(Q\) trapped within the surface \(A\) with the electric flux \(\oint_A \boldsymbol{E} ~\cdot \text{d}\boldsymbol{a}\) through the surface \(A\). The scalar product \(\boldsymbol{E} ~\cdot \text{d}\boldsymbol{a}\) picks out only the portion of the electric field \(\boldsymbol{E}\) parallel to the \(\text{d}\boldsymbol{a}\) element. All other parts are eliminated in the scalar product.

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

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Maxwells Equations

Maxwell equations

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!

Content
  1. ⏲ [00:14] Applications of the Maxwell equations
  2. ⏲ [02:08] Electric field vector
  3. ⏲ [05:12] Magnetic field vector
  4. ⏲ [10:15] Divergence integral theorem - this mathematical theorem combines the volume integral of the divergence of a vector field with the surface integral of this vector field.
  5. ⏲ [10:15] Divergence integral theorem - this mathematical theorem combines the volume integral of the divergence of a vector field with the surface integral of this vector field.
  6. ⏲ [17:50] Curl integral theorem - this mathematical theorem combines the surface integral of the curl of a vector field with the line integral of this vector field.
  7. ⏲ [23:58] The FIRST Maxwell’s equation - states that the charges are sources and sinks of the electric field.
  8. ⏲ [27:46] The SECOND Maxwell’s equation - states that magnetic charges always occur as dipoles. There are no magnetic monopoles.
  9. ⏲ [30:23] The THIRD Maxwell’ equation (Faraday’s law of induction) - states that a time-varying magnetic field generates an electric field and vice versa. This Maxwell equation contain also the Lenz’s rule.
  10. ⏲ [35:02] THE FOURTH Maxwell’s equation - states that the magnetic field can be generated by electric currents and time-varying electric fields (displacement current)

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