Self inductance of a bent coil – Rankers Physics

Self Induction: Practice Problem & Solution

A coil of \(\text{Cu}\) wire (radius \(r\), self inductance \(L\)) is bent in two concentric turns each having radius \(\frac{r}{2}\). The self-inductance now is:
\(2L\)
\(L\)
\(4L\)
\(\frac{L}{2}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Self Induction. Understanding the underlying formula is key to arriving at the correct answer below:

Self-inductance of a coil is \(L \propto N^2 r\). When bent into \(2\) turns of radius \(r/2\), new self-inductance is \(L' \propto (2)^2 (r/2) = 2 L\).

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