You use apparently to emphasize that you are repeating information that you have heard, but that you do not know is definitely true.
1. Mr Andersen is here and would like to see you for a few moments. Apparently it’s rather urgent.
2. Did she really believe this? Apparently she did.
3. Apparently artists and directors alike donate their services.
You can also use apparently when you are describing how something seems to be, even though you are not sure that it is really like that.
4. There are cases where two apparently opposing views may both be correct.
5. He was systematically circling the block, stopping each time, apparently to make sure I was still upstairs.
You use obviously to emphasize that something is easily seen, noticed, or recognized.
6. He had obviously already taken his shower, as his hair was dark with water.
7. Fontane was obviously irritated but trying to be polite for Lucy’s sake.
8. She was looking at him darkly and obviously wanting to speak.
You can also use obviously to introduce something that is easily understood.
9. This will obviously take some time and cost a great deal of money.
10. Obviously parents need to be sensible.