Microfiber Vs Wool Duster which is better in car wash. . .

These are products for cleaning dust. Used to clean the dust in cars. Cleaning with these does not damage the paint, no micro-scratches on the surface. 

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Microfiber: Many people know the use of microfiber cloth in car cleaning. It is made of many small fibers, which rub against the body of the car to produce a kind of static electricity that picks up dirt from the surface, much like pulling a magnetic iron. These microfibers can be washed many times, cleaned, and reused. They are also a bit heavy which makes the car surface clean.

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Wool Duster: The second image in the post is of Wool Duster. These are made primarily from natural sources, such as sheep. These also produce static electricity like microfibers. However, many Wool Dusters can not be washed, if it is dirty, then you have to use them again.
So if you want to buy a cleaning product to use for some time, then microfiber will be the best. And if you want to put a duster next to it, you can also put a Wool Duster.