A coil of wire of radius 'r' has 600 turns and a self-inductance of 108 mH. The self-inductance of a coil with same radius and 500 turns is ______.
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Self-inductance is essentially a measure of magnetic "inertia". Because every turn creates magnetic flux that cuts through every other turn, the effect compounds quadratically ($N \times N$), not linearly!
Step 1: Understanding the Concept:
Self-inductance ($L$) of a coil is directly proportional to the square of the number of turns ($N$), assuming the geometry (radius and length) remains the same. Step 2: Formula Application:
$L \propto N^2 \implies \frac{L_2}{L_1} = \left( \frac{N_2}{N_1} \right)^2$. Step 3: Explanation:
$L_2 = 108 \times \left( \frac{500}{600} \right)^2 = 108 \times \left( \frac{5}{6} \right)^2$
$L_2 = 108 \times \frac{25}{36} = 3 \times 25 = 75$ mH. Step 4: Final Answer:
The self-inductance is 75 mH.