Respuesta :
a) 80 J
b) [tex]1.02\cdot 10^{21}W/m^2[/tex]
c) [tex]2.74\cdot 10^7 V/m[/tex]
d) 0.091 T
Explanation:
a)
The relationship between energy and power is
[tex]P=\frac{E}{t}[/tex]
where
P is the power
E is the energy delivered
t is the time elapsed
In this problem, we have:
[tex]P=2.00\cdot 10^{12} W[/tex] is the average power of the pulse
[tex]t=4.00 ns = 4.00\cdot 10^{-9}s[/tex] is the duration of one pulse of light
Solving for E, we can find the energy given to the cell during this pulse:
[tex]E=Pt=(2.00\cdot 10^{12})(4.00\cdot 10^{-9})=8000 J[/tex]
However, this is the energy spread over 100 cells. So, the energy given to 1 cell is:
[tex]E'=\frac{8000}{100}=80 J[/tex]
B)
The intensity delivered by the pulse is given by
[tex]I=\frac{P}{A}[/tex]
where
P is the power of the pulse
A is the area over which the power is spread
In this problem:
[tex]P=2.00\cdot 10^{12} W[/tex] is the average power of the pulse
The area is the surface area of the cell, which has the shape of a disk, so its area is given by
[tex]A=\pi (\frac{d}{2})^2[/tex]
where
[tex]d=5.00 \mu m = 5.00\cdot 10^{-6} m[/tex] is the diameter of the cell
However, the pulse is spread over 100 cells, so the total area to consider is the area of 100 cells:
[tex]A=100\pi (\frac{d}{2})^2[/tex]
So the intensity is
[tex]I=\frac{P}{100\pi (\frac{d}{2})^2}[/tex]
And substituting we find:
[tex]I=\frac{2.00\cdot 10^{12}}{100\pi (\frac{5.00\cdot 10^{-6}}{2})^2}=1.02\cdot 10^{21}W/m^2[/tex]
c)
The relationship between power of an electromagnetic wave and maximum value of the electric field in the pulse is given by
[tex]P=\epsilon_0 E^2 c[/tex]
where
[tex]\epsilon_0=8.85\cdot 10^{-12}F/m[/tex] is the vacuum permittivity
E is the maximum value of the electric field
[tex]c=3.0 \cdot 10^8 m/s[/tex] is the speed of light
In this problem, we have
[tex]P=2.00\cdot 10^{12}W[/tex] is the average power of the pulse
Therefore, by re-arranging the equation for E, we can find the maximum value of the electric field of the pulse.
It is:
[tex]E=\sqrt{\frac{P}{\epsilon_0 c}}=\sqrt{\frac{2.00\cdot 10^{12}}{(8.85\cdot 10^{-12})(3.0\cdot 10^8)}}=2.74\cdot 10^7 V/m[/tex]
D)
In an electromagnetic wave, the relationship between amplitude of the electric field and amplitude of the magnetic field is given by
[tex]E=cB[/tex]
where
E is the amplitude of the electric field
B is the amplitude of the magnetic field
c is the speed of light
Here we have:
[tex]E=2.74\cdot 10^7 V/m[/tex] is the amplitude of the electric field for this pulse
[tex]c=3.0 \cdot 10^8 m/s[/tex] is the speed of light
Solving the equation for B, we find the maximum value of the magnetic field in the pulse:
[tex]B=\frac{E}{c}=\frac{2.74\cdot 10^7}{3.0\cdot 10^8}=0.091 T[/tex]
