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I followed all of the lines and it was good Physics revision from almost 50 years ago. Very enjoyable.
However for the less technically minded, here is an alternative method if you are prepared to do it yourself.
1. Unwind the solenoid and measure the length of the wire as 77m.
2. Measure the diameter of the wire with a digital caliper to determine it is 26 swg.
3. Buy some 26 swg wire and cut a piece 77m long.
4. Use this to rewind your solenoid.

No maths or physics required

Brilliant, that's a genuinely helpful trick!
I had a wife once who was physic - she knew everything I was going to do beforehand.

Physic (noun): a medicine that purges; cathartic; laxative.
No wonder she knew what you were going to do...

I meant telepathetic

doesn't that mean she worked in a call center

Just because your women are all on call .......

when I was at school if I was naughty they used to send me to the matron to be caned......now I have to spend good money for the same thing!!