Consider a uniformly charged sphere of radius rand total charge q. the electric field eout outsidethe sphere (r≥r) is simply that of a point charge q. the electric field ein inside the sphere (r≤r) is radially outward with field strengthein=1/4πϵ0(q/r^3)rthe electric potential vout outside the sphere is that of a point charge q. find an expression for the electric potential vin at position r inside the sphere. as a reference, let vin=vout at the surface of the sphere. what is the ratio vcenter/vsurface? graph v versus r for 0≤r≤3r.

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.