Question

Write down the properties of electromagnetic waves.

Answer 1

1. Electromagnetic waves are produced by any accelerated charge.
2. Electromagnetic waves do not require any medium for propagation. So electromagnetic wave is a non-mechanical wave.
3. Electromagnetic waves are transverse in nature. This means that the oscillating electric field vector, oscillating magnetic field vector and propagation vector (gives direction of propagation) are mutually perpendicular to each other.
4. Electromagnetic waves travel with speed which is equal to the speed of light in vacuum or free space, c = `1/sqrt(epsilon_0mu_0) 3 xx 10^8 "ms"^-1`
5. The speed of electromagnetic wave is less than speed in free space or vacuum, that is, v < c. In a medium of refractive index,
   `mu_0 = "c"/"v" = (1/sqrt(epsilon_0mu_0))/(1/sqrt(epsilonmu))`
   `=> mu = sqrt(epsilon_"r"mu_"r")`,
6. Electromagnetic waves are not deflected by electric field or magnetic field.
   
7. Electromagnetic waves can show interference, diffraction and can also be polarized.
8. The energy density (energy per unit volume) associated with an electromagnetic wave propagating in vacuum or free space is
   u = `1/2 epsilon_0 "E"^2 + 1/(2mu_0) "B"epsilon^2`
   Where, `1/2`ε₀ E² = u_E is the energy density in an electric field and `1/(2mu_0)` Bε² = u_B is the energy density in a magnetic field. 
   Since, E = Bc ⇒ u_B = u_E.
   The energy density of the electromagnetic wave is = ε E² = -B²
9. The average energy density for electromagnetic wave, ⟨u⟩ = `1/2`ε₀ E² = `1/2 1/mu_0` Bε² 
10. The energy crossing per unit area per unit time and perpendicular to the direction of propagation of the electromagnetic wave is called the intensity.
    Intensity, I = ⟨u⟩c
11. Like other waves, electromagnetic waves also carry energy and momentum. For the electromagnetic wave of energy U propagating with speed c has linear momentum which is given by = `"Energy"/"speed" = "U"/"c"`. The force exerted by an electromagnetic wave on unit area speed of a surface is called radiation pressure.
12. If the electromagnetic wave incident on a material surface is completely absorbed, then the energy delivered is U and momentum imparted on the surface is p = `"U"/"c"`.
13. If the incident electromagnetic wave of energy U is totally reflected from the surface, then the momentum delivered to the surface is ∆p = `"U"/"c" - (- "U"/"c") = 2 "U"/"c"`.
14. The rate of flow of energy crossing a unit area is known as pointing vector for electromagnetic waves, which is `vec"S" = 1/mu_0 (vec"E" xx vec"B") =`c²ε₀ `(vec"E" xx vec"B")`. The unit for the pointing vector is W m^-2. The pointing vector at any point gives the direction of energy transport from that point.
15. Electromagnetic waves carries not only energy and momentum but also angular momentum.