Editing Radiation pressure (section)

=== Radiation pressure from momentum of an electromagnetic wave ===
{{Main|Poynting vector}}
According to Maxwell's theory of electromagnetism, an electromagnetic wave carries momentum.  Momentum will be transferred to any surface it strikes that absorbs or reflects the radiation.

Consider the momentum transferred to a perfectly absorbing (black) surface. The energy flux (irradiance) of a plane wave is calculated using the [[Poynting vector]] {{nowrap|<math>\mathbf{S} = \mathbf{E} \times \mathbf{H}</math>}}, which is the [[cross product]] of the [[electric field]] vector ''E'' and the [[magnetic field]]'s auxiliary field vector (or ''[[Magnetic field#The H-field|magnetizing field]]'') ''H''.  The magnitude, denoted by ''S'', divided by the [[speed of light]] is the density of the linear momentum per unit area (pressure) of the electromagnetic field.  So, dimensionally, the Poynting vector is {{nowrap|1=''S'' = {{sfrac|power|area}} = {{sfrac|rate of doing work|area}} = {{sfrac|{{sfrac|Δ''F''|Δ''t''}} Δ''x''|area}}}}, which is the speed of light, {{nowrap|1=''c'' = Δ''x'' / Δ''t''}}, times pressure, {{nowrap|1=Δ''F'' / area}}.  That pressure is experienced as radiation pressure on the surface:
<math display="block"> P_\text{incident} = \frac{\langle S\rangle}{c} = \frac{I_f}{c}</math>
where <math>P</math> is pressure (usually in [[pascals]]), <math>I_f</math> is the incident [[irradiance]] (usually in W/m<sup>2</sup>) and <math>c</math> is the [[speed of light]] in vacuum.  Here, {{nowrap|{{sfrac|1|''c''}} ≈ {{val|3.34|u=N/GW}}}}.

If the surface is planar at an angle ''α'' to the incident wave, the intensity across the surface will be geometrically reduced by the cosine of that angle and the component of the radiation force against the surface will also be reduced by the cosine of ''α'', resulting in a pressure:
<math display="block"> P_\text{incident} = \frac{I_f}{c} \cos^2 \alpha </math>

The momentum from the incident wave is in the same direction of that wave.  But only the component of that momentum normal to the surface contributes to the pressure on the surface, as given above.  The component of that force tangent to the surface is not called pressure.<ref name="Wright">{{citation | last = Wright | first = Jerome L. | date = 1992 | title = Space Sailing | publisher = Gordon and Breach Science Publishers}}</ref>