Not Really a Homework question, But an Interesting problem

[jmckennon]

Homework Statement

In class today my physics professor proposed this question and left it unanswered:

(We're beginning to study Gauss' Law) "Lightning strikes Manhattan in a brilliant display, each strike delivering some 10,000 amperes of electron flow from the cloud base to the ground. How wide is a lightning strike. Since it can be seen from kilometers away, is it as wide as say, one of the huge manhattan buildings?"

I've beginning thinking about this all day and can't seem to come to any conclusions about it, as i have never really thought about that. My initial thoughts are that the lightning strike seen is actually the flux form the electric field caused by the lightning?

 

[jbsteele]

Homework Equations Gauss' Law:∇⋅E = ρ/ε The Attempt at a SolutionI think that the answer to the professor's question is that the width of the lightning strike is actually the flux from the electric field created by the lightning, rather than the physical width of the strike itself. Since the lightning can be seen from kilometers away, it must be producing a very large electric field with a correspondingly large flux.

 

[baba89]

I find this question very interesting and it is definitely related to the topic we are studying, Gauss' Law. While I cannot give a definitive answer without more information and calculations, I can provide some insights and suggestions to approach this problem.

Firstly, it is important to understand the concept of electric flux and how it relates to Gauss' Law. Electric flux is a measure of the electric field passing through a given area. In simpler terms, it is the number of electric field lines passing through a surface. Gauss' Law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

Now, let's apply this to the lightning strike in Manhattan. The question asks if the lightning strike is as wide as one of the huge buildings in Manhattan. To answer this, we need to estimate the electric field generated by the lightning strike and the charge enclosed by it.

The electric field generated by a lightning strike can reach up to 100 million volts per meter. This is an extremely high value and it can vary depending on the specific conditions of the strike. However, for the sake of simplicity, let's use this value in our calculations.

Next, we need to estimate the charge enclosed by the lightning strike. This can be a bit more challenging as it depends on the specific characteristics of the strike, such as its duration and the size of the cloud. However, we can make some assumptions and estimates based on previous studies and observations. For example, a typical lightning strike can transfer a charge of about 10 coulombs. Again, this value can vary, but it gives us a starting point.

Now, using Gauss' Law, we can calculate the electric flux through a given surface, in this case, the surface of a Manhattan building. This will give us an idea of the width of the lightning strike. However, it is important to keep in mind that the electric field and charge values used in our calculations are estimates and the actual values may vary.

In conclusion, the width of a lightning strike can be estimated using Gauss' Law and some assumptions about the electric field and charge enclosed by the strike. It is a complex problem and the answer may not be exact, but it is a great opportunity to apply our knowledge of physics to a real-life situation. I encourage you to continue thinking about this problem and perhaps even try to calculate the width of the lightning strike yourself.