A coil of wire of radius $r$ has 600 turns and self inductance of $108 \mathrm{mH}$. The self inductance of…

A coil of wire of radius $r$ has 600 turns and self inductance of $108 \mathrm{mH}$. The self inductance of a coil with same radius and 500 turns is
  1. 80 mH
  2. 75 mH
  3. 108 mH
  4. 90 mH

Solution

Self-inductance of a coil $=\frac{N \phi_B}{I}$ $ =\frac{N \frac{\mu_0 I}{2 R} \times \pi R^2}{I}=\frac{\pi \mu_0}{2} \cdot N R $ So, $ \begin{aligned} & \frac{L_2}{L_1}=\frac{N_2}{N_1} \\ & L_2=L_1 \times \frac{N_2}{N_1}=108 \times \frac{500}{600}=90 \mathrm{mH} \end{aligned} $

Asked in: AP EAMCET 2018 (23 Apr Shift 2)

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