The reason why the potato heats up but the paper plate does not is due to the difference in their material properties. Potatoes contain a significant amount of water, which allows them to absorb the microwaves and convert them into heat. The microwave radiation causes the water molecules in the potato to vibrate and generate heat, which cooks the potato.

On the other hand, the paper plate is made of dry, non-polar materials that do not contain water molecules. As a result, the microwaves are not absorbed by the paper plate, and it remains cool. The white color of the paper plate also helps to reflect the microwave radiation, reducing the amount of energy absorbed by the plate.

It is important to note that using any kind of paper or plastic product in a microwave oven can be risky, as they can release chemicals or catch fire if they get too hot. It is generally safer to use microwave-safe materials such as glass or ceramic dishes to heat up food in a microwave oven.