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Let\'s apply the energy density and intensity equations to a laser. In particula

ID: 2035526 • Letter: L

Question

Let's apply the energy density and intensity equations to a laser. In particular, we will consider an industrial laser cutter that is used for cutting through thin sheets of soft materials. It emits a beam with electric-field amplitude Emax=2.76×105V/m over an area of 2.00 mm2. Find (a) the maximum magnetic field Bmax, (b) the maximum energy density umax, (c) the intensity Sav=I of the beam, and (d) the average power of the beam.

a) Find the maximum energy density for a 3000 W laser with an electric-field amplitude Emax=7.08×105N/C.

Express your answer in joules per cubic meter to three significant figures.

Explanation / Answer

a)

Bmax = Emax / C

Bmax = (2.76 x 10^5 N/C) / (3 x 10^8)

Bmax = 9.2 x 10^-4 T

b)

Umax = eo*Emax^2

Umax = 8.854 x 10^-12 x (2.76 x 10^5)^2

Umax = 0.674 J/m^3

Uavg = Umax / 2 = 0.337 J/m^3

c)

I = Sav = Uavg x C

I = 0.337 J/m^3 x 3 x 10^8 m/s

I = 1.01 x 10^8 w/m^2

d)

Pavg = (1.01 x 10^8 w/m^2 x 2 x 10^-6 m^2)

Pavg = 202 W

A)

E_max = 7.08 x 10^5 N/C

maximum energy density = eo*E_max^2

= 8.854 x 10^-12 x (7.08 x 10^5)^2

= 4.438 J/m^3