A laser has a power of 23.4 W and a beam radius of 0.523 mm (a) Find the intensi

Question

A laser has a power of 23.4 W and a beam radius of 0.523 mm (a) Find the intensity of the laser. W/m2 (b) Suppose you were floating in space and pointed the laser beam away from you. What would your acceleration be? Assume your total mass, including equipment, is 73.5 kg and that the force is directed through your center of mass. Hint: The change in momentum is the same as in the nonreflective case. m/s2 (c) Calculate your acceleration if it were due to the gravity of a space station with mass 1.20 x 106 kg and center of mass 114.3 m away m/s2 (d) Calculate the peak electric and magnetic fields of the laser. Emax Bmax = N/C If you were planning to use your laser welding torch as a thruster to get you back to the station, don't bother because the force of gravity is stronger. Better yet, get somebody to toss you a line.

Explanation / Answer

given laser power, P = 23.4 W

beam radius r = 0.523 nm

a. intensity = P/pi*r^2 = 23.4/pi*(0.523*10^-9)^2 = 2.723*10^19 W/m^2

b. momentum of a photon = h*v/c ( where v is frequency of photon and c is its speed)

if n photons leave laser per second, then force due to laser = nhv/c

but laser power = n*hv

hence force F = P/c = 23.4/3*10^8 N = 7.8*10^-8 N

mass m = 73.5 kg

hence acceleration a= F/m = 1.0612244*10^-9 m/s/s

c. for M = 1.2*10^6 kg

r = 114.3 m

F = GMm/r^2 = ma

a = GM/r^2 = 6.67*10^-11*1.2*10^6/114.3^2

a = 6.12653*10^-9 m/s/s

d. now I = Em^2/c*mu*2

2.723*10^19 = Em^2/3*10^8*4*pi*10^-7*2

Em = 143286204184.9808 V/m

also

Em/Bm = c

Bm = 477.62068 T

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