Question

In: Physics

You have a vertical thick line representing a line source emitting 10^6 photons per second per...

You have a vertical thick line representing a line source emitting 10^6 photons per second per cm. With "P" at some distance away.

A) Write the equation representing the DIFFERENTIAL contribution to the particle fluence rate at "P".

B) Using the results for (A), determine the particle fluence rate if the vertical thick line is 240cm long. The upper segment is 160cm long and the lower is 80cm long. The point "P" is 200cm from the line source (at its closest).

Expert Solution

consider a small elemnt of the source dx at a distance x from the origin

let be the emission rate of the souce per unit length

Total phtons emitted by the element = dx and these photons are emitted in 4 solid angle

Fluence rate at P due to this element

= dx/4(l² + x² )

we get the total fluence rate by the full length of the source by integrating the above expresssion from

-x₁ to x₂

B) we put the values

= 1.0e+6 ; l = 200 cm ; x1 = 80 cm ; x2 = 160 cm

fluence rate = 1.0e+6 /4 *200 { arcTan (160/200) + arcTan (80/200) }

= 419.86 particles /sq.cm/s

genius_generous answered 2 years ago

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