A regular light Bulb Emits waves of various wavelengths (which makes the \"white

Question

A regular light Bulb Emits waves of various wavelengths (which makes the "white" light); The distribution of Intensities is a Continuous Function of the wavelength (as in the Discussion of Black Body Radiation). This distribution, however, peaks at some Characteristic wavelength. In the following Assume that the Entire Power of the Light Bulb comes from emitting in this Single Characteristic Wavelength. A light Bulb has a P=100W.

1.) What is the Intensity of the Emitted Light at a distance r = 10m from the Light Bulb?

2.) What is the Amplitude of the Electromagnetic Field at that Distance?

3.) What is the Average Energy Density of the e.m. radiation at the distance r =10m from the light bulb?

4.) What is the momentum transferred by this light to a small flat mirror with surface area S= 0.5m2 placed in front of the light bulb at the distance r = 10m during the time t= 1s?

5.) What is the Pressure exerted by the light on the Surface from number 4?

Explanation / Answer

Given power of light   P = 100 W a) intensity of the emitted light at distance    r = 10 m is             I = P / A                 = 100 W / 4r 2                    = 100 W / 4*100                  = 0.0795 W / m 2   b)    maximum amplitude of electromagnetic field                  Emax B max = 2 o I                                      = 2 ( 4*10-7 ) ( 0.0795 )                                      = 1.998*10^ -7   V/m* T   c) average energy density of e.m. radiation at the distance r=10m from
the light bulb.                u = I / c                    =   0.0795 / 3*10 ^8 m/s                     = 2.65*10^ -10 J / m 3       d )       momentum   transfererd is                      p = Energy / c                         = P . t / c                            = 100 * 1 s / 3*10 8 m/s                            = 3.33*10-7 kg m /s    e)   pressure P = I / c                              = 0.0795 / 3*10 8                              = 2.65*10^ -10 Pa Given power of light   P = 100 W a) intensity of the emitted light at distance    r = 10 m is             I = P / A                 = 100 W / 4r 2                    = 100 W / 4*100                  = 0.0795 W / m 2   b)    maximum amplitude of electromagnetic field                  Emax B max = 2 o I                                      = 2 ( 4*10-7 ) ( 0.0795 )                                      = 1.998*10^ -7   V/m* T   c) average energy density of e.m. radiation at the distance r=10m from
the light bulb.                u = I / c                    =   0.0795 / 3*10 ^8 m/s                     = 2.65*10^ -10 J / m 3       d )       momentum   transfererd is                      p = Energy / c                         = P . t / c                            = 100 * 1 s / 3*10 8 m/s                            = 3.33*10-7 kg m /s    e)   pressure P = I / c                              = 0.0795 / 3*10 8                              = 2.65*10^ -10 Pa                              = 2.65*10^ -10 Pa

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