The number of turns in a solenoid is doubled, and at the same time its length is doubled.

(a) Does the magnetic field within the solenoid increase, decrease, or stay the same?

(b) Choose the best explanation from among the following:

I. Doubling the number of turns in a solenoid doubles its magnetic field, and hence the field increases.

II. Making a solenoid longer decreases its magnetic field, and therefore the field decreases.

III. The magnetic field remains the same because the number of turns per length is unchanged.