(b) Self-motivation
Self-motivation is the inner force that drives a person to achieve goals without external pressure, lure, reward, or appreciation from others.
Source: Session 3: Self-motivation, Chapter 2
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The key phrase in the question is "inner urge… without any external pressure / lure for award or appreciation" — this directly matches the textbook definition of self-motivation: "our ability to do the things that need to be done without someone or something influencing us."
Only (b) Self-motivation fits the definition of an internal drive with no external reward needed.