Power in beam of light given amplitude

[Cspeed]

I would like to calculate the power of a beam of light once I know the electric field amplitude. For example if I know the amplitude along a line from -1 meter to +1 meter every 0.5 m is [1, 2, 2.5, 2, 1 V/m], how can I find the power from this is? Is there enough info? (it's in vacuum/air) Thank you.

 

[mfb]

Energy density is proportional to the squared amplitude (see Wikipedia for example), and power is just average energy density times the speed of light. Don't forget the magnetic component, which is 50% of the total power.

 

[Cspeed]

Thanks, but I'm not sure still. I knew that power was proportional to the square of amplitude, but I'm hoping to get a figure in watts. I see that I need H as well. But how does this all fit into my 1-D scenario?

 

[mfb]

You get W/m^2 - what else did you expect? If the source emits radiation uniform in space, you can multiply that with the corresponding sphere surface area to get the total power.

 

[sardar]

To calculate the power of a beam of light, we need to know the intensity of the light, which is directly related to the electric field amplitude. The power of a beam of light can be calculated using the formula P = I*A, where P is the power, I is the intensity, and A is the cross-sectional area of the beam.

In this case, we have the electric field amplitude along a line from -1 meter to +1 meter with a spacing of 0.5 meters. To calculate the power, we first need to calculate the intensity. The intensity of light is given by the formula I = c*ε0*E^2, where c is the speed of light in vacuum (approximately 3x10^8 m/s) and ε0 is the permittivity of free space (approximately 8.85x10^-12 F/m). Therefore, the intensity at each point can be calculated by squaring the electric field amplitude and multiplying it by the constants c and ε0.

Once we have calculated the intensity at each point, we can then calculate the total power by summing up the intensities at each point and multiplying it by the cross-sectional area of the beam. In this case, the cross-sectional area would be the area of a rectangle with a width of 0.5 meters and a length of 2 meters (from -1 meter to +1 meter).

However, please note that the calculation above assumes that the beam of light is uniform and does not take into account any variations in the electric field amplitude along the beam. To get a more accurate calculation, we would need to have the electric field amplitude at every point along the beam and integrate it over the entire cross-sectional area.

In conclusion, there is enough information provided to calculate the power of the beam of light, but the accuracy of the calculation may vary depending on the assumptions made about the beam.