We can reasonaly model a 75 W incandescent lightbulb as a sphere 6 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?
ok..once again I am totally confused.
radius = 3*10^-2 meters
calculate surface area 4 pi r^2
Intensity of visible = .05 * 75 / surface area
I = Emax Bmax /(2 uo) = (Emax)^2/(2 uo c)
I am sure this is in your Physics book!!! Look up intensity of electromagnetic wave and "Poynting vector".
No problem, I can help explain the steps to solve this problem.
To find the visible light intensity at the surface of the bulb, we first need to determine the total power emitted by the bulb as visible light. We are given that only 5% of the energy goes to visible light, so we can calculate the total power emitted by the bulb as:
Total power emitted = 0.05 * 75 W
Now, we need to calculate the surface area of the bulb. Since the bulb is modeled as a sphere with a diameter of 6 cm, we can use the formula for the surface area of a sphere:
Surface area = 4 * π * r^2
Where r is the radius of the sphere (which is half the diameter).
Once we have the surface area, we can use it to calculate the visible light intensity at the surface of the bulb:
Visible light intensity = Total power emitted / Surface area
For part (b) of the question, we need to calculate the amplitudes of the electric and magnetic fields at the surface of the bulb for a sinusoidal wave with the calculated intensity.
For a sinusoidal wave, the intensity is related to the amplitude of the electric and magnetic fields by the following equation:
Intensity = (ε_0 * c) / 2 * sqrt(ε_r * μ_r) * E^2
Where ε_0 is the vacuum permittivity, c is the speed of light in a vacuum, ε_r is the relative permittivity of the medium, μ_r is the relative permeability of the medium, and E is the amplitude of the electric field.
We can rearrange this equation to solve for E:
E = sqrt((2 * Intensity) / (ε_0 * c) * sqrt(ε_r * μ_r))
To calculate the amplitude of the magnetic field, we can use the relationship between the electric and magnetic fields in an electromagnetic wave:
E/B = c
Therefore, B = E/c.
Now, with the calculated electric field amplitude, we can find the magnetic field amplitude.
I hope this explanation helps clarify the steps needed to solve the problem. Let me know if you have any further questions!