Chapter : 8

What are Electromagnetic Waves ?

Topic

Displacement Current

Formula

$$\text{I}_\text{D}= \epsilon_\text{0}\frac{\text{d}\phi_\text{E}}{\text{dt}}\\ \space\space\space\space\space\space\text{or} \\ \frac{\text{dq}}{\text{dt}}=\epsilon_\text{0}\frac{\text{d}\phi}{\text{dt}}$$

Symbol Representation

ID = Maxwell’s displacement current

 Φ = Electric flux

(dΦ/dt) = Rate of change of
electric flux

Important Points

  • When electric field or electric flux change with time, ID comes in the picture.
  • ID does not exist in steady condition in a region.
  • ID does not flow through the conducting wire.
  • ID produce magnetic field in a region.

Electromagnetic waves

$$\text{c}=\frac{1}{\sqrt{\mu_0\epsilon_0}}\\=3×10^8\text{ms}^{-1}\\ \oint\vec{\text{B}}.\vec{\text{dl}}=\mu_0(\text{I}+\text{I}_\text{D})\\=\mu_0(\text{I}+\frac{\epsilon_0\text{d}\phi_\epsilon}{\text{dt}})\\ (\text{Ampere-Maxwell law}) \\ \oint\vec{\text{E}}\vec{\text{ds}}=\frac{\text{q}}{\epsilon_0}\\ \text{Gauss law in electrostate}$$

$$\oint\vec{\text{B}}.\vec{\text{ds}}=0\\ \text{(Gauss law in magnetostate)} \\ \oint\vec{\text{E}}.\vec{\text{dl}}=\frac{\text{-df}}{\text{dt}}\int_s \vec{\text{B}}\vec{\text{ds}} \\ \text{(Faraday’s law of EM induction)}$$

c = speed of light

μ0 = permeability constant = 4π × 10-7H/m
ε0 = Vacuum permittivity = 8.85 × 10-12C2/N.m2
b

= magnetic field

= integral over closed
path

I = conduction current

ID = displacement current

$$\bull\space \text{Electric field} \vec{(\text{E})} \text{and magnetic field} \\\vec{(\text{B})} \text{are at right angle to each other}\\ \space \text{as well as right angle to the}\\ \text{direction of wave propagation}. $$

Example: radio waves, microwaves,
infrared waves etc.

  • Speed of EM, in vacuum, is equal to speed of light.
  • Oscillating or accelerated charge
    produced EM.
  • EM waves are transverse in nature (Maxwell).
  • EM wave do not require any
    medium for propagation.

$$\bull\space \vec{\text{E}} \space\text{and} \space\vec{\text{B}} \space\text{are in same phase (in EM)}. $$

  • Velocity of EM wave entirely
    depends on electric and magnetic
    field of medium.
  • Energy carried by EM wave equally divide between

$$\space \vec{\text{E}} \space\text{and} \space\vec{\text{B}}$$

  • EM waves are not deflected by
    electric and magnetic field.

EM spectrum

  • Orderly distribution of EM radiations according to their wavelength or frequency.