A two-dimensional electrostatic field varies with the coordinates x and y, but is independent of z. Show that the average value of the potential V on any circle in the x-y plane is equal to the value of the potential at the center of the circle provided that there is no charge inside the circle. [Hint: Consider a circle of uniform charge per unit length lambda=Q/(2*pi*a). Find V at a point outside the circle in two ways: using Gauss' law, and by direct integration. Do not carry out this last integral; just set it up. Now look at the equality between the integral and the result of Gauss' law, and interpret what it is saying.