AN ACR LTT; ON A DEP RADAR VECTOR FAILS TO CAPTURE THEIR OUTBOUND RADIAL. A FLC HDG TRACK POS DEV. CTR CTLR ALERTS THEM TO THE DEV.

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AFTER DEP FROM CHS WE WERE CLRED TO BRUNSWICK VOR (SSI) VIA THE SSI 2. WE WERE FLYING A 180 DEG HDG TO INTERCEPT THE 218 DEG RADIAL OFF CHS TO SSI. APPROX 15 NM FROM CHS STILL ON A HDG OF 180 DEGS; ZJX NOTIFIED US THAT WE HAD ALREADY PASSED THE AIRWAY; ALTHOUGH OUR NAV WAS SHOWING US THAT HAD YET TO INTERCEPT. ATC ADVISED US TO TURN TO 240 DEGS TO INTERCEPT. SINCE I DOUBTED MY NAV; ATC GAVE ME A HDG TO BRUNSWICK (SSI) AND DIRECT WHEN ABLE. MY COPLT AND I TURNED OFF AND ON THE #1 NAV. ONCE ESTABLISHED TOWARD SSI; I ASKED ZJX WHAT RADIAL THEY SHOWED ME ON. THEY REPLIED THE 218 DEG RADIAL TO OR 038 DEG RADIAL FROM SSI; WHICH AT THAT TIME WAS WHAT I WAS SHOWING. WE PROCEEDED DIRECT TO SSI; THEN CONTINUED ON COURSE. I HAVE NO EXPLANATION ON HOW OR WHY THE CDI REMAINED PEGGED ON THE L WHEN WE HAD ALREADY PASSED THE AIRWAY. LATER TESTS ON THE NAV THAT DAY REVEALED NO DISCREPANCIES WITH THE EQUIP. AT THE TIME OF THE SIT. I ASKED ZJX CTR IF IT CREATED ANY PROBS AND SHE SAID 'NO PROBS AT ALL.' SHE WAS QUITE HELPFUL. TO PREVENT THIS PROB IN THE FUTURE; I WILL VERIFY THAT THE #2 NAV IS SET UP AND XCHKED WITH NAV #1 BEFORE PROCEEDING. THIS WILL REVEAL A POTENTIAL PROB BEFORE IT BECOMES ONE.