Potter derivative of LOTR? No!

[hfakhro at nyc.rr.com]

Hello -

I just forced a friend to read the Potter books, and right after she 
finished them, her boyfriend made her read the Lord of the Rings. She 
is now convinced that Rowling's work is purely derivative from LOTR. 
I keep blubbering that indeed it is not, but I can't find compelling 
arguments, and was wondering if anyone here had any suggestions as to 
what I could tell her.

Rowling herself has said that she was not fond of LOTR (something 
like, not having read them more than once so that meant they weren't 
her favourites.) She also has said that she would never claim to have 
invented a whole mythology like Tolkien did, but that she thinks she 
has better jokes. (True, IMO).

My friend insists that regardless of what Rowling says, some of the 
similarities are as follows: Wormtail is a tribute to Wormtongue 
(character and name), Dumbledore is Gandalf, and the Black Riders are 
the source for Dementors. Among other things she also says that 
Rowling took some names from Tolkien such as Longbottom (I can't 
remember the others that she mentioned.) She also thinks that Rowling 
filched elements from the world itself such as wizards, elves, 
goblins, etc and made them behave similarly in her books. This is a 
more general question (and I feel a bit stupid asking) but aren't 
wizards, goblins, elves etc ancient creations before Tolkien? I.E. he 
didn't invent them either did he?

I don't think Wormtail is similar to Wormtongue, because Wormtongue 
was sent to the king directly from (sorry forgot his name - the good 
wizard who went bad) whereas Wormtail went bad only after being 
friendly with MPP (as far as we know anyway.) But having read LOTR 
only once, I can't come up with good arguments, so if there is anyone 
here who knows the books well, do share your expertise, please! Must 
defend JKR's integrity!

Thanks,
Hella