What would a newer dime be worth when one side is copper and the other side is normal ?
there is no silver in a dime, it's copper and zinc. Sounds like you might have gotten an oddity that might be worth something to a collector. Take it to a coin shop and ask there.
. . .10?
A dime is worth its face value, unless it is a very rare item, which is rarely ever the case. The silver in the coin is worth very little. This is because the government aims to prevent the coin's intrinsic value being greater than its face value.