Question

A "laser cannon" of a spacecraft has a beam of cross-sectional area A. The maximum electric field in the beam is 2E. The beam is aimed at an asteroid that is initially moving in the direction of the spacecraft. What is the acceleration of the asteroid relative to the spacecraft if the laser beam strikes the asteroid perpendicularly to its surface, and the surface is not reflecting

Answer 1

Acceleration of the asteroid relative to the spacecraft = 2ε
`E^(2)`A/m

Step-by-step explanation:

The maximum electric field in the beam = 2E

cross-sectional area of beam = A

The intensity of an electromagnetic wave with electric field is

I = cε
`E_(0) ^(2)`/2

for
`E_(0)` = 2E

I = 2cε
`E^(2)` ....equ 1

where

I is the intensity

c is the speed of light

ε is the permeability of free space

`E_(0)` is electric field

Radiation pressure of an electromagnetic wave on an absorbing surface is given as

P = I/c

substituting for I from above equ 1. we have

P = 2cε
`E^(2)`/c = 2ε
`E^(2)` ....equ 2

Also, pressure P = F/A

therefore,

F = PA ....equ 3

where

F is the force

P is pressure

A is cross-sectional area

substitute equ 2 into equ 3, we have

F = 2ε
`E^(2)`A

force on a body = mass x acceleration.

that is

F = ma

therefore,

a = F/m

acceleration of the asteroid will then be

a = 2ε
`E^(2)`A/m

where m is the mass of the asteroid.