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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# High-power lasers are used to compress a plasma (a gas of charged particles) by radiation pressure. A laser generating radiation pulses with peak power ${\mathbf{1}}{\mathbf{.5}}{\mathbf{×}}{{\mathbf{10}}}^{{\mathbf{3}}}{\mathbf{\text{MW}}}$ is focused onto 1.00 mm2 of high-electron-density plasma. Find the pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths.

Pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths is $1×{10}^{7}Pa$

See the step by step solution

## Step 1: Listing the given quantities

Power of radiation $P=1.5×{10}^{3}MW$

Area A=1.00 mm2

## Step 2: Understanding the concepts of radiation pressure formula

Substituting the given values of power, area, and speed of light in the radiation pressure formula, we can find the pressure exerted on the plasma due to the light beams.

Thrust applied on plasma is given as-

${\mathbf{F}}{\mathbf{=}}\frac{\mathbf{2}\mathbf{IA}}{\mathbf{c}}$

Here, I is the intensity of radiation, A is the cross-sectional area and c is the speed of light in vacuum.

## Step 3: Calculations of the pressure exerted on the plasma

The force acting on the plasma, due to radiation, is-

$F=\frac{2IA}{c}$

The radiation pressure Pr is given as-

$\begin{array}{c}{p}_{r}=\frac{F}{A}\\ =\frac{2IA}{cA}\\ =\frac{2I}{c}\end{array}$

The intensity is $I=\frac{P}{A}$

P is power; A is the total area intercepted by the radiation.

$\begin{array}{c}{p}_{r}=\frac{2P}{Ac}\\ =\frac{2\left(1.5×{10}^{9}W\right)}{\left(1×{10}^{-6}{m}^{2}\right)\left(3×{10}^{8}\text{\hspace{0.17em}m}/\text{s}\right)}\\ =1×{10}^{7}Pa\end{array}$

Pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths is $1×{10}^{7}Pa$