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
where θ is the angle of incidence and d the distance from the source.)
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
where h is the height of the particle above the plane of the circle. Find h, for maximum attraction. (Compare with Problem 72 above)
In Problem 73 above, if the wire has instead the form of a square of side , the attraction is proportional to
Find h for maximum attraction.