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].
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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