The very long coil exists with the following information .
$$ a:=\text{radius of the circle of the coil} $$
$$ n:=\text{number of turns of the coil per unit length} $$
$$ x:=\text{lenght of the coil(not a length of the wire )} $$
$$ N:=nx ~~ \leftarrow~~ \text{total number of turns of the coil} $$
$$ I:=\text{current which is to be flown to the coil} $$
We want to know the force of shrink of the coil .
$$ H=nI ~~ \leftarrow~~ \text{magnetic field inside the coil } $$
$$ \Phi=\underbrace{\mu_{0}H}_{\text{Wb}/\text{m} ^{2} } \cdot \underbrace{\pi a ^{2}}_{\text{m}^{2} } \cdot \underbrace{nx}_\text{turns} ~~ \leftarrow~~ \text{interlinkage mangtic flux} $$
$$ U_{\text{m} } = \frac{1}{2} I \Phi_{} ~~ \leftarrow~~ \text{energy} $$
\$~ \delta x ~~ \leftarrow~~ \text{extent of length of shrink} ~\$
\$~ \delta n ~~ \leftarrow~~ \text{incremented number of turns per unit length as shrink is done } ~\$
What I can't get currently is the below equation .
$$ \delta n \cdot x + n \cdot \delta x =0 $$
What should I consider first?