Which is the longest and which is the shortest day in the Northern Hemisphere and why?

On which dates does the sun shine vertically overhead at:

(a) Equator
(b) Tropic of Cancer
(c) Tropic of Capricorn

Why are days and nights equal at all places on earth on September 23? What are the seasons in the Northern and the Southern Hemispheres on this date?

What is meant by Summer Solstice? When do we have Summer Solstice in the Northern Hemisphere?