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parameters express value message
turns in a metre n turn/m  
radius m  
length m  
self inductance \(L_0=\mu _0 \pi l a^2 n^2\)
short coil inductance \(\frac{L}{L_0}=\frac{\left(\frac{l^2}{a^2}+4\right) K\left(-\frac{4 a^2}{l^2}\right)}{3 \pi }+\frac{\left(4-\frac{l^2}{a^2}\right) E\left(-\frac{4 a^2}{l^2}\right)}{3 \pi }-\frac{8 a}{3 \pi l}\)