The inductance L of a solenoid is proportional to the square of the number of turns, whereas

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The inductance L of a solenoid is proportional to the square of the number of turns, whereas the energy stored in the solenoid PEind is proportional to L.
(a) If the length of the solenoid is doubled, by what factors do L and PEind change?
(b) Explain physically why the factors in part (a) are larger than 2.

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