- #1

Pushoam

- 962

- 52

## Homework Statement

## Homework Equations

Radiation pressure i.e.R.P is the instantaneous pressure exerted by radiation on a perfectly absorbing surface perpendicular to the propagation vector of the radiation.

Maxwell has shown that R.P = u , (1) where u is energy density

R.P = F/A, (2)

F ##\hat n## = dp/dt ##\hat n## , (3)

**S =**εc

^{2}

**E×B**= εc

^{2}EB ##\hat n## = cu##\hat n##, (4)

## The Attempt at a Solution

Using eqns. 1,2,3,4

R.P.= u =

__EB εc__= F/A = (dp/dt)/A =

__lim (Δp/Δt)/A: Δt→0__

ε EB = ## \lim_{Δt \rightarrow 0}\frac{ Δp}{c A ~Δt}##:

Since change in the momentum is in the direction of poynting vector, we can write,

ε

**E×B**= ## \lim_{Δt \rightarrow 0}\frac{ Δp}{c A ~Δt}\hat n## i.e. change in the momentum per unit volume , (5)

Now, according to the book,

change in the momentum i.e. Δp ##\hat n##=

**p**

_{v}( c A Δt),

where

**p**

_{v}is the momentum density

So, ε

**E×B =**

**p**_{v}, (6)

Now, my question is : momentum density means momentum per unit volume or change in momentum per unit volume?

I think momentum density is the momentum transported to the surface by the radiation , when the energy contained in one unit volume of the radiation gets absorbed by the surface.

So, here momentum density is change in the momentum per unit volume, not momentum per unit volume.

Is this correct?