Following up on Mean minimum distance for N random points on a one-dimensional line and Mean minimum distance for N random points on a unit square (plane), I have the following questions.

Given N random points in the unit square, what is the expected value of the Maximum distance between any two such points?

I know that the expected value of the distance is $\Big(2 + \sqrt{2} + 5 \log (1+ \sqrt{2}) \Big)$ and the (mysterious) distribution of the distances is given by the square line picking distribution (http://mathworld.wolfram.com/SquareLinePicking.html).

Thank you!