**Characteristics of EM waves:**

1. Electromagnetic waves are transverse in nature. They are produced by varying electric and magnetic fields. In an electromagnetic wave, the electric and magnetic fields oscillate perpendicular to each other as well as perpendicular to the direction of propagation of the wave. Both electric and magnetic fields vary in phase with each other.

For an electromagnetic wave travelling in positive x direction.

E_{y} = E_{0} sin (ωt – kx)

B_{z} = B_{0} sin (ωt – kx)

Where ω = 2π/T = 2πv and k = 2π/λ

2. In 1865 Clerk Maxwell postulated the existence of a new current called displacement current which is due to varying electric field with time. This current exists even in vaccum.

3. Speed of electromagnetic waves in free space \(c=\frac{1}{\sqrt{{{\mu }_{0}}{{\in }_{0}}}}\).

In a material medium, the speed is \(v=\frac{1}{\sqrt{\mu \in }}\).

4. Average energy densities of electric and magnetic fields of an electromagnetic wave \({{u}_{e}}=\frac{1}{4}{{\in }_{0}}E_{0}^{2}\) and \({{u}_{m}}=\frac{1}{4}\frac{B_{0}^{2}}{{{\mu }_{0}}}\).

Where Eₒ and Bₒ are the amplitudes of electric and magnetic fields. Also \({{B}_{0}}=\frac{{{E}_{0}}}{c}=\sqrt{{{\mu }_{0}}{{\in }_{0}}}{{E}_{0}}\).

∴ u_{e} = u_{m}

Total average energy density is \(\mu ={{u}_{e}}+{{u}_{m}}=\frac{1}{2}{{\in }_{0}}E_{0}^{2}=\frac{B_{0}^{2}}{2{{\mu }_{0}}}\).

5. Intensity of an electromagnetic wave in a medium I = ϵₒvE²_{rms}

In vaccum: I = ϵₒcE²_{rms}

**Maxwell equations:**

a) \(\oint{\overline{E}\,\overline{dA}=\frac{Q}{{{\in }_{0}}}}\) [Gauss Law for Electricity].

b) \(\oint{\overline{B}\,\overline{dA}=0}\) [Gauss Law for Magnetism].

c) \(\oint{\overline{E}\,\overline{dl}=\frac{d{{\phi }_{B}}}{dt}}\) [Faraday’s Law].

d) \(\oint{\overline{B}\,\overline{dl}}={{\mu }_{0}}{{i}_{c}}+{{\mu }_{0}}{{\in }_{0}}\frac{d{{\phi }_{E}}}{dt}\) [Ampere – Maxwell’s Law].