Solid angles and particle velocities

  • Thread starter quarky2001
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  • #1
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This should be a simple question, but I haven't found a clear explanation anywhere yet.

Suppose that there are a bunch of particles in a gas, with their velocities "uniformly distributed over solid angles", and I want to find out what fraction of particles are traveling with velocities in a certain angular range.

Conceptually, I know what this means. I'm just not sure how to do it - I drew a diagram.

Suppose the shaded area represents 20% of the sphere's total surface area. How do find the angle theta?

attachment.php?attachmentid=31859&stc=1&d=1296657266.jpg
 

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Answers and Replies

  • #2
tiny-tim
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hi quarky2001! :smile:

(have a theta: θ :wink:)

that's called a cap of a sphere of radius θ …

i cant remember the formula for its area :redface:, but it's fairly easy to find by integration :wink:
 

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