Yes, for the six-month period between its sunrise about September 21 and its sunset about March 21 the daylight time lasts 24 hours at the South Pole.
The same is true at the North Pole, and the events occur on the same days, in opposition.
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It's because the Earth's axis is tilted. If the axis were perpendicular to the orbit, daylight would last 12 hours every day, pretty well everywhere on Earth. Because the Earth's axis is tilted the amount of daylight depends on the latitude. Try to visualize the Earth rotating around its axis; when the north pole points away from the Sun, the Sun is always below the horizon from the point of view of somebody at the north pole. For somebody at the south pole, the Sun will always be above the horizon (at that time of the year). For locations in between, the days get longer and longer as you move - in this example - from the north pole towards the south pole.
On the last day of summer at the North Pole, the sun is still above the horizon for 24 hours, so there is continuous daylight with no darkness. This phenomenon is known as the midnight sun.
To get from the South Geographic Pole to the South Magnetic Pole, you would need to head northwards. The South Magnetic Pole is located in Antarctica, but it is not at the exact geographic South Pole.
This difference in daylight hours between Alaska and South Carolina is due to their difference in latitude. Alaska is located much further north, near the Arctic Circle, where the summer days are longer due to the tilt of the Earth's axis. South Carolina, being closer to the equator, experiences more consistent day length throughout the year.
The last magnetic pole reversal, when the north and south magnetic poles switched places, occurred about 780,000 years ago. This is based on geological evidence and the study of magnetic patterns in rocks and sediments.