Originally Posted by
misspelledDino
Perhaps you aren't feeling it in your quads because the weight is too light?
Also, the low bar back squat is primarily a posterior chain (glutes, adductors, ham strings) movement. It does train quads too, but the quads aren't the prime movers. So I wouldn't expect you to 'feel the quads' unless the weight was super heavy for you (it's not) at which point you'd feel the quads, glutes, adductors, hamstrings and everything else.
The main reason we train the low bar back squat (as opposed to high bar or some other variant) is because it trains the most muscle mass across the largest range of motion. Thus the movement is superior to all other squat variants in getting big and strong as quickly as possible. It is, after all, your life and your training and you can squat however you wish. But I'd advise you reconsider moving to high bar squats.
One other thing while I'm doling out unsolicited advice...you injuring your back doing squats makes me suspect you have unresolved form issues. You might consider filming a squat set and posting on the SSC Q&A sub forum for a form check.
Good luck with your training.