Why does antenna tuner in crystal radio use capacitor and an inductor?
You are very astute. You can indeed construct a crystal set without a physical capacitor, relying instead on the capacitance of the antenna alone and tuning by varying the inductance. Of course, the value of inductance required will vary with the length of the antenna. Reckon on 10 pF per metre as a starting point. Perhaps a variable capacitor is popular because it can be arranged to dominate the antenna capacitance and make tuning less antenna length dependent. A wide range, reliable variable inductor can also present challenges. Go ahead and experiment.