Is F=1/l√T/m dimentionally correct?

no it is not correct dimensionally

Explanation:

f=1/l√T/m

taking square on both side in order to remove square root

f²=T/l²m

f=ma =kgm/sec²

therefore

kg.m/sec²=sec/m².kg

kg.m=sec*sec²/m².kg

kg.m=sec³/m².kg

kg=sec³/m³.kg

so the equation is incorrect dimensionally

small = small current large mag large current

b.a device that inputs heat into a cool object