Problem 72
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is
 

$I = \dfrac{k \sin \theta}{d^2}$

 

where θ is the angle of incidence and d the distance from the source.)

Solution:

 

Problem 73
It is shown in the theory of attraction that a wire bent in the form of a circle of radius a exerts upon a particle in the axis of the circle (i.e., in the line through the center of the circle perpendicular to the plane) an attraction proportional to
 

$\dfrac{h}{(a^2 + h^2)^{3/2}}$

 

where h is the height of the particle above the plane of the circle. Find h, for maximum attraction. (Compare with Problem 72 above)

Solution:

 

Problem 74
In Problem 73 above, if the wire has instead the form of a square of side $2l$, the attraction is proportional to
 

$\dfrac{h}{(h^2 + l^2)\sqrt{h^2 + 2l^2}}$

 

Find h for maximum attraction.

Solution:

 
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