Consider $($negatively charged$)$ DNA in an ionic solution $($assume equal numbers of positive and negative ions in the solution$),$ as illustrated in the picture to the right.

Part $($a$)$

Why don't positive ions attach all along the length of the DNA until the DNA is electrically neutral? What, if anything, opposes that process?

Part $($b$)$

The positive cloud of ions surrounding the negatively charged DNA extends a distance $D,$ the "Debye length." Just outside the Debye length, is the electric field magnitude smaller or larger than it would be if not for the positive ionic cloud? Why?

Part $($c$)$

Does the presence of the ions in solution make it harder or easier for two pieces of DNA floating around in solution to get close together $($compared to the case of pure water$)?$ Why?

Part $($d$)$

Explain how the Debye length changes with temperature and salt concentration and give an argument as to why these dependencies are plausible.