Question

A small helium-neon laser emits red visible light with a power of 3.80 mW in a beam that has a diameter of 2.70 mm.

(a) What are the amplitudes of the electric and magnetic fields of the light?

E_{max} |
= V/m |

B_{max} |
= T |

(b) What are the average energy densities associated with the
electric field and with the magnetic field?

u_{E,av} |
= J/m^{3} |

u_{B,av} |
= J/m^{3} |

(c) What is the total energy contained in a 1.00-m length of the
beam?

J

Answer #1

Given Data:

P = 3.80 mw = 3.80 x 10^{-3} W

D = 2.70mm = 2.70 x 10^{-3} m

Part A:

laser intensity I = P/A

I = 4P/D^{2}

I = (4*3.80 x 10^{-3})/[3.14*(2.70 x
10^{-3})^{2}]

I = 664.028 W/m^{2}

and we also know that I = ½*_{o}*c*E^{2}

E = sqrt(2I/oc)

E = sqrt(2*664.028/8.854 x 10^{-12}*3 x
10^{8})

E = sqrt(499983.43)

**E _{max} = 707.1 V/m**

and

B = E/c

B = (707.1)/(3 x 10^{8})

**B _{max} = 2.357 x 10^{-6} T**

Part 2:

uB_{av} = uE_{av} =
¼*e_{o}*E^{2}_{max}

uB_{av} = ¼*8.854 x
10^{-12}*707.1^{2}

uB_{av} = 1.1 x 10^{-6} J/m^{3}

Part 3:

E_{tot} = u_{tot}*V

E_{tot} = 2*u_{E}*0.25**D^{2}*L

E_{tot} = 2*1.1 x
10^{-6}*0.25*3.1415*0.0027^{2}*1

E_{tot} = 1.2589 x 10^{-11} J

**E _{tot} = 1.26 x 10^{-11} J**

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