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Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 2.09\times 10^{11}~\text{V/m}2.09×10 ​11 ​​ V/m for a time of 1.00 ns. What energy does it deliver on a 1.00~\mathrm{mm^2}1.00 mm ​2 ​​ area?

Respuesta :

Answer:

The energy it delivers is 5.799x10⁴J

Explanation:

Given data:

Em = maximum electric field = 2.09x10¹¹V/m

t = time = 1 ns = 1x10⁻⁹s

A = area = 1 mm² = 1x10⁻⁶m²

Question: What energy does it deliver, E = ?

First, you need to calculate the intensity of the wave:

[tex]I=\frac{c\epsilon *E_{m}^{2} }{2}[/tex]

Here

c = speed of light = 3x10⁸m/s

ε = permittivity = 8.85x10⁻¹²C²/N m²

Substituting:

[tex]I=\frac{3x10^{8}*8.85x10^{-12}*(2.09x10^{11})^{2} }{2} =5.799x10^{19}W/m^{2}[/tex]

The energy:

[tex]E=IAt=5.799x10^{19}*1x10^{-6}*1x10^{-9}=5.799x10^{4}J[/tex]

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