How Can Maxwell's Equations Estimate Oscillating Fields Near a Light Bulb?

[hasan_researc]

Homework Statement

Make an order-of-magnitude estimate of the (magnitude of the) oscillating optical-frequency electric and magnetic fields in the vicinity of a light bulb.

Homework Equations

I have no idea as to what equations I should be using!

The Attempt at a Solution

No idea at all! This is a hopelessly difficult task

 

[hikaru1221]

This is just a suggestion. I'm also really unsure about the question.

For a common incandescent light bulb, the radiation it emits is mostly near/in visible spectrum. This is just my speculation, because if it mostly emits ultraviolet or infrared rays, it harms people and thus wouldn't be used widely. If we know the range of electromagnetic radiation that the light bulb emits the most, we get the answer to the question easily.

Anyway, we should find some way to deduce that the frequency that the light bulb most emits is near the visible range. So now it's your turn:
1. Taking the idea of Wien's displacement law, which gives us the wavelength that a black body emits the most (by solving $$\frac{\partial u}{\partial \lambda}=0$$), we can find the frequency of the peak of emission from black bodies, by solving $$\frac{\partial u}{\partial f}=0$$. Note that the peak wavelength doesn't correspond to the peak frequency.
2. Assume that the light bulb is a black body. A common light bulb has operating temperature of about 3000K. From here, find the peak frequency of light bulb. This will give you the answer.

 

[fluidistic]

This is just a suggestion. I'm also really unsure about the question.

For a common incandescent light bulb, the radiation it emits is mostly near/in visible spectrum. This is just my speculation, because if it mostly emits ultraviolet or infrared rays, it harms people and thus wouldn't be used widely. If we know the range of electromagnetic radiation that the light bulb emits the most, we get the answer to the question easily.

Mostly infrared I'd say. See http://en.wikipedia.org/wiki/Light_bulb#Efficiency_comparisons.

Anyway, we should find some way to deduce that the frequency that the light bulb most emits is near the visible range. So now it's your turn:
1. Taking the idea of Wien's displacement law, which gives us the wavelength that a black body emits the most (by solving $$\frac{\partial u}{\partial \lambda}=0$$), we can find the frequency of the peak of emission from black bodies, by solving $$\frac{\partial u}{\partial f}=0$$. Note that the peak wavelength doesn't correspond to the peak frequency.
2. Assume that the light bulb is a black body. A common light bulb has operating temperature of about 3000K. From here, find the peak frequency of light bulb. This will give you the answer.

Seems interesting. I'll investigate what is the "u" function.

 

[hikaru1221]

Mostly infrared I'd say. See http://en.wikipedia.org/wiki/Light_bulb#Efficiency_comparisons.

Yep. By "infrared", I mean radiation whose wavelength is very far from visible range (visible range is so narrow, so most of the time, things emit mostly radiation out of that range). My rough calculation showed that the peak wavelength is a bit above 750nm, so strictly speaking, it lies in infrared range, but saying in a "tricky way", I'll say it lies near the visible range

I'll investigate what is the "u" function.

Sorry for not clarifying it earlier. It's specific radiative intensity of black bodies (I'm not sure how it's called in English).
And, to the OP, note that the "u" functions in those 2 equations are different.

 

[paranormal]

As a scientist, it is important to approach problems with a systematic and analytical mindset. In this case, we can use Maxwell's equations to estimate the magnitude of oscillating electric and magnetic fields near a light bulb. The equations that are relevant to this problem are:

1. Gauss's Law for electric fields: ∇⋅E = ρ/ε0, where E is the electric field, ρ is the charge density, and ε0 is the permittivity of free space.

2. Ampere's Law for magnetic fields: ∇×B = μ0(J+ε0∂E/∂t), where B is the magnetic field, J is the current density, μ0 is the permeability of free space, and ∂E/∂t is the time derivative of the electric field.

3. Faraday's Law: ∇×E = -∂B/∂t, where E is the electric field and B is the magnetic field.

To make an order-of-magnitude estimate, we can make some simplifying assumptions. First, we can assume that the light bulb is a point source and the electric and magnetic fields decrease with distance according to the inverse square law. Second, we can assume that the electric field is primarily due to the electric potential difference across the light bulb, and the magnetic field is primarily due to the current flowing through the bulb.

Based on these assumptions, we can estimate the magnitude of the electric and magnetic fields at a distance r from the light bulb as follows:

1. Electric field: We can estimate the charge density ρ by considering the amount of charge that flows through the light bulb per unit time (i.e. the current) and the time it takes for the charge to pass through the bulb. Let's assume a current of 1 ampere and a time of 1 millisecond for simplicity. This gives us a charge density of ρ = 1 coulomb/0.001 seconds = 1000 coulombs/second. Plugging this into Gauss's Law and solving for E, we get E ~ ρ/ε0r^2 ~ (1000 coulombs/second)/(8.85 x 10^-12 coulombs^2/(newton x meter^2)) = 1.13 x 10^14 newtons/coulomb.

2. Magnetic field: We can estimate the current density J by considering