1. A square of paper measuring a on a side carries a total charge +q which is uniformly distributed over its surface. The square lies in the x-y plane with its center at the origin and its sides parallel to the coordinate axes. Find the electric field on any point on the y-axis with y > a. Show that this square looks like a point charge for the case y>> a.
2. The electric charge of the proton is not concentrated at a point but rather distributed over a volume. According to experimental investigations at the Stanford Linear Accelerator, the charge distribution of the pro- ton can be approximated by an exponential function
ep= ____ e^((-r)/b)8(pi)b
where r is the radial position inside the proton and b is a constant equal to 0.23 x 10^(-15)m. Find the electric field as a function of the radial distance. What is the magnitude of the electric field at r =1 x 10^(-15)m? Compare the electric field strength you find to that of a point charge of magnitude e. At what distances r do these two differ by 10% or more?