1. (25 pts/5pts each part) The figure shows a spherical shell with uniform volume charge density o = 1.76 nC/m', inner radius a = 15.0 cm, and outer radius b = 2.20a. What is the magnitude of the electric field (in N/C) at the following radial distances? (a) r = a/2.00 Qenc = 0 , so E = 0 (b) r = a Qenc = 0 , so E = 0 (c) r = 1.50a Only some of the total charge of the shell is contained in the Gaussian surface. Qenc = 0*Vsphere =[1.76 *101-9 C/m'] *4/3*pi*[(1.5a^3) - a^3] Area of Gaussian Surface = 4*pi* (1.5a)^2 E = Qenc/(Area of Gaussian Surface x Free Space Permittivity] = 10.5 N/c (d) r=b All of the total charge of the shell is contained in the Gaussian surface. Qenc = 0*Vsphere =[1.76 *101-9 C/m'] *4/3*pi*[(b^3) - a^3] Area of Gaussian Surface = 4*pi* (b)^2 E = Qenc/(Area of Gaussian Surface x Free Space Permittivity] = 19.8 N/c (e) r= 3.00b(2) 10. The "trapping web" and "variable circular plot" methods are both analyzed in program Distance as a point sample where animals further from the point are weighted less in the calculation of density than nearby animals because: a) animals can not be detected far from the point b) the areas of concentric rings increases with radial distance from the point c) the truncation function discounts animals that are far away animals fly or run away from the point because the observer is there e) a bird in the hand is worth two in the bush (2) 11. Population estimation programs that use data collected from transects utilize statistical procedures to fit a to the data in order to account for animals that were to distant from the transect to be detected a) variable circular plot b) probability density function c) change in ratio frequency index e) chi-square contingency table