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March 15th, 2013, 10:13 AM   #1
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Help with probability problem

A particle is emitted in a random, 3 dimensional direction from point A. A sphere of radius X is located a distance R from point A. What is the probability, in terms of X and R, that the particle will collide with the sphere?

I'm not sure how to figure this question out and would appreciate any help.
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March 15th, 2013, 12:30 PM   #2
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Re: Help with probability problem

Assuming that the particle emission is isotropic, you need to compute the solid angle subtended by the sphere where the solid angle is centered at the point of emission. The probability is the solid angle/4?.
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March 15th, 2013, 01:12 PM   #3
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Re: Help with probability problem

Thanks! How do I go about finding the solid angle?
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March 16th, 2013, 12:56 PM   #4
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Re: Help with probability problem

Quote:
Originally Posted by overture3d
Thanks! How do I go about finding the solid angle?
Because of symmetry the main step can be done in plane geometry.
Pass a plane through the particle point and the center of the sphere. The intersection of the plane with the sphere is a (great) circle. Get the tangents from the particle point to the circle. This gives you an angle in the plane.

The solid angle is the cone angle obtained by rotating the plane angle around the source - center line. I suspect it might not be necessary. The plane angle divided by 2? will do.
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