Why multiple coils on a ferrite rod antenna?
Here is a link to a bunch of AM radio schematics.  A common theme is that the loopstick antenna is either a transformer or an autotransformer, tuned to resonate at the desired broadcast frequency by one-half of a dual-gang variable capacitor that also tunes the local oscillator.  As above, this covers (in theory), two of the three coils in your image.
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