Question

Show that the self-inductance per unit length of an infinite, straight, thin wire is infinite.

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Given:

Here, we are to prove that the self-inductance per unit length of the given wire goes to infinity. We let,

Wire radius: rSelf-inductance: LCurrent: IMagnetic field: BSurface area: aLength: lMagnetic flux: Φ\begin{align*} &\text{Wire radius:~} r\\ &\text{Self-inductance:~} L \\ &\text{Current:~} I\\ &\text{Magnetic field:~} B \\ &\text{Surface area:~} a \\ &\text{Length:~} l \\ &\text{Magnetic flux:~} \Phi \end{align*}

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