Properties of EM waves
- Velocity of EM waves in free space or vacuum is a fundamental constant.
- Experimentally it was found that the velocity of EM wave is same as speed of light(c=3x108m/s).
- The value of c is fundamental constant.
- Therefore , c=(1/√μ0ε0)
- No material medium is necessary for EM waves. But they can propagate with ina medium as well.
- EM waves require time varying electric and magnetic fields to propagate.
- If the medium is present then velocity v = (1/√με)
- Whereμ =permeability of the medium and ε=permittivity of the medium.
- For example: -Spectacles. When light falls on glass of the spectacle, light rays pass through glass.i.e. Light waves propagate through medium which is glass here.
- EM waves carry energy and momentum.
- Total energy stored per unit volume in EM wave ET= E2ε0(partly carried by electric field and partly by magnetic field).
- As EM waves carry energy and momentum, it becomes an important property for its practical purposes.
- EM waves are used for communication purposes, voice communication in mobile phones, telecommunication used in radio.
- EM waves exert pressure. As they carry energy and momentum, they exert pressure.
- The pressure exerted by EM waves is known as Radiation pressure.
- For example: -
- The sunlight which we get from sun is in the form of visible light rays.
- These light rays are also part of EM waves.
- If we keep our palm in sun,after some time, palm becomes warm and starts sweating.
- This happens because sunlight is getting transferred in the form of EM waves and these EM waves carry energy.
- Suppose total energy transferred to the hand =E.
- Momentum = (E/c) as c is extremely high, therefore momentum is very small.
- As momentum is very less, pressure experiencedis also very less.
- This is the reason due to which the pressure exerted by the sun is not experienced by the hand.
Problem:- In a plane electromagnetic wave, the electric field oscillates sinusoidal at a frequency of 2.0 × 1010 Hz and amplitude 48 V m−1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density
of the B field. [c = 3 × 108 m s−1.]
Frequency of the electromagnetic wave, ν = 2.0 × 1010 Hz
Electric field amplitude, E0 = 48 Vm−1
Speed of light, c = 3 × 108 m/s
(a) Wavelength of a wave is given as:
= (3 × 108)/ (2.0 × 1010)
(b) Magnetic field strength is given as:
B0 = (E0/c)
= (48)/ (3 × 108)
(c) Energy density of the electric field is given as:
UE = (1/2) (E2ε0)
And, energy density of the magnetic field is given as:
ε0 = Permittivity of free space
μ0 = Permeability of free space
We have the relation connecting E and B as:
E = cB ... (1)
c= (1/√μ0ε0) … (2)
Putting equation (2) in equation (1), we get
E= (1/√μ0ε0) B
Squaring both sides, we get
E2=1/ (μ0ε0) B2
ε0E2 = (B2/μ0)
(1/2)ε0E2 = (1/2)μ 0B2