You have uncommitted changes on my_branch that you want to commit to master, without committing all the changes from my_branch.
Example
git merge master
git stash -u
git checkout master
git stash apply
git reset
git add example.js
git commit
git checkout .
git clean -f -d
git checkout my_branch
git merge master
git stash pop
Explanation
Start by merging master into your branch, since you'll have to do that eventually anyway, and now is the best time to resolve any conflicts.
The -u option (aka --include-untracked) in git stash -u prevents you from losing untracked files when you later do git clean -f -d within master.
After git checkout master it is important that you do NOT git stash pop, because you will need this stash later. If you pop the stash created in my_branch and then do git stash in master, you will cause needless merge conflicts when you later apply that stash in my_branch.
git reset unstages everything resulting from git stash apply. For example, files that have been modified in the stash but do not exist in master get staged as "deleted by us" conflicts.
git checkout . and git clean -f -d discard everything that isn't committed: all changes to tracked files, and all untracked files and directories. They are already saved in the stash and if left in master would cause needless merge conflicts when switching back to my_branch.
The last git stash pop will be based on the original my_branch, and so will not cause any merge conflicts. However, if your stash contains untracked files which you have committed to master, git will complain that it "Could not restore untracked files from stash". To resolve this conflict, delete those files from your working tree, then git stash pop, git add ., and git reset.