(Solved): 2. Consider a hollow sphere of radius r with uniform surface charge density +. (a) (5 pts.) A sm ...

2. Consider a hollow sphere of radius $$r$$ with uniform surface charge density $$+?$$. (a) (5 pts.) A small triangular pyramid, side length a which is smaller than $$r$$, is placed centered completely inside the sphere (see figure a). What is the flux through each face of the triangular pyramid? How do you know it? (b) (10 pts.) A larger triangular pyramid, side length $$b$$ which is larger than $$r$$, completely surrounds the sphere. The center of the sphere and center of the triangular pyramid coincide. What is the flux through each face of the triangular pyramid? Hint: Gauss's law is our friend. (c) (10 pts.) A point charge is to be placed in the center of the sphere/pyramid configuration from part b. What should the magnitude of the charge be to make the total flux through the large triangular pyramid equal $$\frac{?8?r^2?}{{?}_0}$$ ? (a)