1. Shown in the left side figure, is the differential solid angle d2 subtended by the differential area dA when viewed from point P. We define the solid angle at point P as the projection of the surface on a sphere of unit radius surrounding the point. Thus, the differential solid angle d2 subtended by surface dA in the left side fig- ure below is given by dN= dn = (dA ·Q)/r² . a) Use this definition to compute the solid angle N subtended by a circular disk of radius a at a point P that is lo- cated a distance R from the disk, where P lies on the normal n passing through the center of the disk, as shown in the right figure. b) Find 2 as a → ∞. [Ans.: b) Hemisphere].

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 32AR
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1. Shown in the left side figure, is the differential solid angle d2 subtended by the
differential area dA when viewed from point P. We define the solid angle at point
P as the projection of the surface on a sphere of unit radius surrounding the point.
Thus, the differential solid angle d2 subtended by surface dA in the left side fig-
ure below is given by dN= dQ = (dA )/r² . a) Use this definition to compute
the solid angle Q subtended by a circular disk of radius a at a point P that is lo-
cated a distance R from the disk, where P lies on the normal n passing through the
center of the disk, as shown in the right figure. b) Find 2 as a → o. [Ans.: b)
Hemisphere].
Questions and Problems
593
R
n
dA
P!
Transcribed Image Text:1. Shown in the left side figure, is the differential solid angle d2 subtended by the differential area dA when viewed from point P. We define the solid angle at point P as the projection of the surface on a sphere of unit radius surrounding the point. Thus, the differential solid angle d2 subtended by surface dA in the left side fig- ure below is given by dN= dQ = (dA )/r² . a) Use this definition to compute the solid angle Q subtended by a circular disk of radius a at a point P that is lo- cated a distance R from the disk, where P lies on the normal n passing through the center of the disk, as shown in the right figure. b) Find 2 as a → o. [Ans.: b) Hemisphere]. Questions and Problems 593 R n dA P!
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