The average radiation on a surface by a normally electromagnetic wave is _______ in case of complete absorption by the surface.
Radiation Pressure on Absorbing Surfaces
When an electromagnetic wave interacts with a surface, it exerts a force on that surface. This force per unit area is known as radiation pressure. The effect of radiation pressure is due to the momentum carried by electromagnetic waves.
Momentum Transfer and Radiation Pressure
An electromagnetic wave carries both energy and momentum. The energy flux (energy per unit area per unit time) of an electromagnetic wave is given by its intensity, \(I\). The momentum per unit volume (\(p_V\)) of an electromagnetic wave is related to its energy density (\(u\)) by the relation \(p_V = u/C\), where \(C\) is the speed of light in vacuum.
The intensity \(I\) of an electromagnetic wave is also equal to the energy density multiplied by the speed of light, i.e., \(I = uC\). From this, we can write \(u = I/C\).
Therefore, the momentum density \(p_V\) can also be expressed as:
\[p_V = \frac{u}{C} = \frac{I/C}{C} = \frac{I}{C^2}\]
Now, consider a surface on which an electromagnetic wave is normally incident. The amount of momentum hitting a unit area of the surface per unit time is equivalent to the momentum contained in a volume of \(C \times 1 \text{ m}^2\) (since the wave travels \(C\) meters in 1 second).
So, momentum per unit area per unit time = \(p_V \times C = \frac{I}{C^2} \times C = \frac{I}{C}\).
Radiation Pressure for Complete Absorption
When an electromagnetic wave is completely absorbed by a surface, all the momentum carried by the wave is transferred to the surface. According to Newton's second law, force is the rate of change of momentum. Therefore, the force exerted on the surface per unit area, which is the radiation pressure (\(P\)), is equal to the momentum transferred per unit area per unit time.
For complete absorption, the average radiation pressure \(P\) is given by:
\[P = \frac{\text{Momentum transferred per unit area per unit time}}{\text{Area}}\]
Since the momentum transferred per unit area per unit time is \(I/C\), the average radiation pressure \(P\) for complete absorption is:
\[P = \frac{I}{C}\]
Where:
- \(P\) is the average radiation pressure.
- \(I\) is the average intensity of the electromagnetic wave (power per unit area).
- \(C\) is the speed of light in vacuum (approximately \(3 \times 10^8 \text{ m/s}\)).
This formula indicates that the radiation pressure is directly proportional to the intensity of the electromagnetic wave and inversely proportional to the speed of light.
Summary of Radiation Pressure Formulas
It is important to distinguish between complete absorption and complete reflection:
- Complete Absorption: If the surface completely absorbs the electromagnetic wave, the radiation pressure \(P\) is \(P = \frac{I}{C}\). In this case, all the incident momentum is transferred.
- Complete Reflection: If the surface completely reflects the electromagnetic wave, the radiation pressure \(P\) is \(P = \frac{2I}{C}\). This is because the momentum of the wave reverses direction, leading to a change in momentum that is twice the incident momentum.
Based on the question asking for the case of complete absorption by the surface, the correct formula for the average radiation pressure is \(P=\frac{I}{C}\).
Important Questions from Electromagnetic Wave Propagation
For sky waves, following statements are given:
(A) n > 1, this shows 81 \(\rm\frac{N}{f^2}\) positive
(B) n > 1, show 81 \(\rm\frac{N}{f^2}\) Negative
(C) n < 1 shows 81 \(\rm\frac{N}{f^2}\) < 1
(D) v g x v p= c 2
(E) n = 0 shows 81 \(\rm\frac{N}{f^2}\) = 1, f = f c
Choose the correct answer from the options given below:
If the Polarization vector is given as N and the Direction of propagation is given as K then which one of the following relations is correct?
The wave length (λ) in meters of an electromagnetic wave is related to its frequency (f) in MHz as:
Bending of light wave as it passes between material of different optical density
The wave impedance of a medium is equal to:
