We can reasonably model a 90-w incandescent lightbulb as a sphere 5.7 cm in diameter. typically, only about 5% of the energy goes to visible light; the rest goes largely to nonvisible infrared radiation.(a) what is the visible light intensity (in w/m^2) at the surface of the bulb? (b) what are the amplitudes of the electric and magnetic fields at this surface, for a sinusoidal wave with this intensity?

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Explanation:

Given quantities:

where is the efficiency of the lightbulb (visible light is 5% of the total power), is the total power of the lightbulb, r is the radius of the lightbulb in meters.

Intensity is power divided by area:

a) Now the effective power is , therefore:

b) Now the intensity is the average poynting vector is related to the magnitudes of the  maximum electric field and magnetic field amplitudes, following:

now and are related:

and

replace in

we replace the values and we get:

therefore