Indeed and that's exactly why this combination is so valuable.
Well, thousands. First you would need to ask yourself what kind of physics that you like can be used in engineering. Than think of your branch:
http://en.wikipedia.org/wiki/List_of...ering_branches
I am totally a electronic guy and if you look what role electronic devices play in the current world, you don't have to think twice about how many possible jobs I could to. But I would not underestimate the opportunities in the other fields. Mechanical engineering might sound old fashioned, but new materials like carbon fiber has let to new ways of construction.
In practice I see my job as very product centered, it is very much about the path from problem to solution. You start by finding our what the problem is, sometimes the hardest part as tasks are often not well defined. From there you start searching for previous solutions for similar problems. You need than to pick your solution, either by formal analysis or from experience (or both). Then you start implementing and finally test your work against your expectations. All this is a continuous task. Your task might change during implementations, new problems or specification are added to your task. Test might show you some faults in your analysis. Then you need to redo some of your work, but hopefully not all.
One of the things I like the most is that you can quickly see how your work improves. You start with an unsolved problem and step by step you end up by something that works. And a good engineer always ends up with something that works or with a clear statement why it doesn't or even better why it can't work. This is quite important if you think about becoming an engineer, you need deep inner interest in understanding how things work, why things work and why some don't. And you will sometime hate your job if things don't work as you want to and finding out why they don't work is probably one of the hardest task. Fining new solutions is also hard but it is far more enjoyable. And you will never search for the same solution twice, but you will search for the same errors over and over again.
And as I said, you earn good money, at least in the field of electronics and I think also in mechanics. The reason is simple, there is a much higher demand then there are good engineers. Of course this implies that you are good in what you do.