Does the sun ever set in the north pole during June 21?

From the viewpoint of a hypothetical observer at the North Pole, we would see the Sun rise very slowly about March 21, and slowly spiral up around the sky. By June 21, the Sun would appear to be about 23 degrees above the horizon, and would circle the sky every 24 hours. From June 21 on, the Sun would continue to circle the sky as it slowly set, reaching the horizon about September 21. (Refraction effects - the bending of light as it passes through the atmosphere - might cause the Sun to appear a day early and to set a day late.)

There would be a week or so of twilight, as the Sun crept further below the horizon, but by September 27 it would be dark and cold, and it would remain that way until mid-March.

There is no land at the North Pole; the Arctic Ocean extends several hundred miles in every direction. So there are no real observers _at_ the North Pole.