The company where you work has obtained and stored five lasers in a supply room. you have been asked to determine the intensity of the electromagnetic radiation produced by each laser. the laser beams have uniform intensity distributions over their cross sections. the lasers are marked with specifications, but unfortunately different information is given for each laser. assume that the laser beams have uniform intensity distributions over their cross sections. part a laser a: power = 2.2 w ; diameter of cylindrical beam = 2.9 mm . calculate the intensity for the laser. part b laser b: amplitude of electric field = 440 v/m . calculate the intensity for the laser. part c laser c: amplitude of magnetic field = 8.2 × 10−6 t. calculate the intensity for the laser. part d laser d: diameter of cylindrical beam = 1.8 mm ; force on totally reflecting surface = 9.0 × 10−8 n. calculate the intensity for the laser. part e laser e: average energy density in beam = 3.0 × 10−7 j/m3. calculate the intensity for the laser. part f rank the lasers in order of decreasing intensity. rank from largest to smallest. to rank items as equivalent, overlap them. laser alaser blaser claser dlaser e smallestlargest

a)  I = 5.79 10⁵ W/m² , b)  I = 2.58 10² W / m², c)   I = 8.03 10³ W / m² , d)     I = 5.3 10⁶ W / m², e)  I = 9 10¹ W / m² , f)  D> A> C> B> E

Explanation:

The intensity is defined as the power per unit area

       I = P / A

The area of a circle is

      A = π r²

Laser A

Power P = 2.2 W

Diameter d = 2.9 mm = 2.9 10⁻³ m

Let's calculate

Area

      A =  π d² / 4

     A =  π (2.2 10⁻³)²/4

     A = 3.80 10⁻⁶ m²

Let's calculate the intensity

     I = 2.2 / 3.80 10⁻⁶

     I = 0.579 10⁶ W / m²

     I = 5.79 10⁵ W/m²

Laser B

The electric field is E = 440 V / m

Intensity average is

      I = E B / 2 μ₀

The relationship of the fields with the speed of light

      E / B = c

The intensity  

       I = EE / 2 μ₀ c

       I = 440² / (2 4π 10⁻⁷ 3 10⁸)

      I = 1.936 105/750

      I = 2.58 10² W / m²

Laser C

The magnetic field amplitude B = 8.2 10⁻⁶ T

      I = c / 2μ₀  B²

      I = 3 10⁸/2 4π 10⁻⁷ (8.2 10⁻⁶)²

      I = 8.03 10³ W / m²

Part D

Diameter d = 1.8 mm = 1.8 10⁻³ m

The radius is r = d / 2 = 0.9 10⁻³ m

The force is F = 9.0 10⁻⁸ N

The radiation pressure is on a reflective surface is

         P = 2S / c

         I = S =P c / 2

The definition of pressure is

         P = F / A

          I = F c / 2 A

          I = 9.0 10⁻⁸ 3 10⁸ / (2π (0.9 10⁻³)²)

          I = 5.3 10⁶ W / m²

Part E

Average energy density

         u = 3.0 10⁻⁷ J / m³

          I = S = c u

          I = 3 10⁸ 3.0 10⁻⁷

          I = 9 10¹ W / m²

Part F

Sort in descending order

The order is

  D> A> C> B> E

resonant frequency