How will my boss know of i am working for someone else?

Your boss will know only if someone else tells him/her or he/she sees you working the second job. There is no database where this can be checked.

Why would he even care?

As long as you show up on time and do your job, what difference would it make to him? Almost every body has another job these days

Unless you signed a contract stating you would not work for a competitor, nothing he can do about it

If you work for someone else he/she will know