How to apply a drop shadow on an object outer borders only?

Question

Let's say we have a ring on a transparent background:

My question is: how I put a drop shadow on this object's external borders only?

If I apply a plain Drop Shadow effect, I get the following, which is not what I want since the internal borders also have a drop shadow.:

Answer 1

1. Apply a drop-shadow as in your second example.
2. Go to the blending options for the drop-shadow effect.
3. Tick the box which says: "Layer mask hides effects".

4. You can now use selection tools to select the inner drop-shadow circle of your layer
5. With this inner drop shadow selected, you can mask it out.

6. Invert the mask, if necessary with Ctrl / Cmd+i

Answer 2

Your drop shadow is going to come from a separate object that shares the outside circumference minus the void in the middle.

or, you can use the quick select tool to only highlight the outside, include the inside, modify the edge to make it cleaner, etc etc..