(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How will a coil's self inductance change if you unwind it and then re-wind half of the length of wire into a coil with the same diameter but with half of the number of turns?

The answer is that it will decrease by 1/4, but I don't understand why it isn't 1/2 instead.

2. Relevant equations

phi (magnetic flux) = LI (where L is inductance, I is current)

n = N/l where "l" is length

B = mew naught * n * I

3. The attempt at a solution

original: L = phi/I = (NBAcostheta) / I = (N* mew naught *n*I*costheta) / I

Now the L with the proposed change: L' = (N/2)* mew naught * ((N/2) / (l/2))* costheta = 1/2 L

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# Inductance of a coil

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