A)
B) 0.531 V/m
C)
D)
Explanation:
A)
The intensity of an electromagnetic wave is given by
where
I is the intensity
P is the power of the wave
A is the area over which the radiation is spread
In this problem:
is the power of the light emitted by the laser
This power spread over a cylindrical beam, so the area over which it spreads is the area of the base of the cylinder, which is the area of a circle:
where
is the diameter of the beam
Therefore, the intensity of the laser beam is:
B)
The relationship between power of an electromagnetic wave and maximum value of the electric field is the following:
where
P is the power
is the vacuum permittivity
is the speed of light
E is the maximum value of the electric field
In this problem we have:
is the power of the light emitted by the laser
is the vacuum permittivity
is the speed of light
Solving for E, we find the value of the electric field:
C)
For an electromagnetic wave, the relationship between amplitude of the electric field and amplitude of the magnetic field is:
where
E is the maximum value of the electric field
c is the speed of light
B is the maximum value of the magnetic field
In this problem we have:
E = 0.531 V/m is the maximum value of the electric field
is the speed of light
Solving the equation for B, we find the maximum value of the magnetic field:
D)
The energy density of an electromagnetic wave is the amount of energy per unit volume of the wave.
The average energy density of an electromagnetic wave is related to the amplitude of the electric field by the equation:
where
w is the energy density
is the vacuum permittivity
E is the maximum value of the electric field
Here we have for this laser beam:
is the vacuum permittivity
E = 0.531 V/m is the maximum value of the electric field
Substituting, we find the average energy density of the laser beam: