In the normal scheme of things, one Page Directory is associated with each process. Whenever a process context switch happen, the Page Directory physical address is load into a designated register (sometimes it is CR3). Per process Page Directory physical address is maintained in the Process Block for that Process.
In addition to this, the address of Page Directory is also mapped to some system defined Virtual address. This address typically remain same for all the process. So the system would do all the necessary initialization to facilitate this mapping.
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