Question

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 1.52\times 10^{11}~\text{V/m}1.52×10 ​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?

Answer 1

30643 J

Step-by-step explanation:

`\mu_0` = Vacuum permeability =
`4\pi * 10^(-7)\ H/m`

t = Time taken = 1 ns

c = Speed of light =
`3* 10^8\ m/s`

`E_0` = Maximum electric field strength =
`1.52* 10^(11)\ V/m`

A = Area =
`1\ mm^2`

Magnitude of magnetic field is given by

`B_0=(E_0)/(c)\\\Rightarrow B_0=(1.52* 10^(11))/(3* 10^8)\\\Rightarrow B_0=506.67\ T`

Intensity is given by

`I=(cB_0^2)/(2\mu_0)\\\Rightarrow I=(3* 10^8* 506.67^2)/(2* 4\pi * 10^(-7))\\\Rightarrow I=3.0643* 10^(19)\ W/m^2`

Power, intensity and time have the relation

`E=IAt\\\Rightarrow E=3.0643* 10^(19)* 1* 10^(-6)* 1* 10^(-9)\\\Rightarrow E=30643\ J`

The energy it delivers is 30643 J