WPA PSK Key in pcap/cap files?

I downloaded a pcap file from wireshark (example) with the Password: Induction and the SSID: Coherer. The WPA-PSK is supposed to be "a288fcf0caaacda9a9f58633ff35e8992a01d9c10ba5e02ef df8cb5d730ce7bc". I searched the file by changing all text to hex and it didn't find it in the cap file. I then tried changing the PSK to CHAR and it still didn't find it in the original file. However in regular text you see Coherer throughout the file. So how do you find exactly where the WPA key is located in the cap files/pcap files..

I am trying to make a program that will Generate sample files (cap/pcap/etc). I have already reproduced the WPA Key based off the SSID/Password and it matches many online generators.

Not exactly sure what you are trying to achieve, but the WPA PSK does not appear in packets broadcast on the network... It is generated independently by the client and access point, then used to encrypt the packet data.