# Electromagnetic Wave Formulas

Electromagnetic waves are a result of vibrations between an electric field and a magnetic field. In other words, Electromagnetic waves are composed of oscillating magnetic and electric fields. In this article, we will see some important electromagnetic wave formulas which will also help you in preparation for competitive exams like JEE and NEET.

Index

## Maxwell’s equations

$$\oint E \cdot dA=Q/\varepsilon _{0}\; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;$$(Gauss’s Law for electricity)

$$\oint B \cdot dA=0 \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;$$(Gauss’s Law for magnetism)

$$\oint E \cdot d\iota =\frac{-d\phi B}{dt} \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;$$(Faraday’s Law)

$$\oint B \cdot dl= \mu_{0}i_{c} + \mu_{0} \epsilon_{0}\frac{d\phi_{E}}{dt}\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\;$$(Ampere-Maxwell Law)

## Oscillating Electric and Magnetic fields

$$E=E_{x}(t)=E_{0}\; sin\; (KZ-\varpi t)$$

$$= E_{0}\; sin\; \left [ 2\pi \left ( \frac{z}{\lambda }-vt \right ) \right ]=E_{0}\; sin\left [ 2\pi \left ( \frac{z}{\lambda }-\frac{t}{T} \right ) \right ]\; \; E_{0}/B_{0}=c$$

$$c=1\sqrt{ \mu_{0} \epsilon_{0} }\; \; \; \;$$, c is speed of light in vaccum

$$v=1/\sqrt{\mu \epsilon }\; \; \; \;$$, v is speed of light in medium

$$p=\frac{U}{c}$$, energy transferred to a surface in time t is U, the magnitude of the total momentum delivered to this surface (for complete absorption) is p

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