Answer
The larger coil has four times the self-inductance.
Work Step by Step
Equation 30.6 gives the self-inductance of a coil.
In this example, the number of turns N is the same.
We see that L is proportional to the flux due to the current through each turn of the coil. The tightly wound loops with the same number of turns will produce the same magnetic field strength inside, so the flux is proportional to the cross-sectional area.
The coil with twice the radius has 4 times the cross-sectional area of the other coil, so its self-inductance is four times as much.
