Question

# How many turns of wire would be required to make a 130-mHinductance out of a 30.0-cm-long air-filled coil with a diameter of5.2 cm?

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How many turns of wire would be required to make a 130-mHinductance out of a 30.0-cm-long air-filled coil with a diameter of5.2 cm?

2021-02-21

Self inductance of an air coredsolenoid $$(L=130mH)$$ depends on
1. the total no. ofturns (N) of the solenoid
2. the length $$(l=30 cm)$$ of the soldnoid
3. the area of thecross section $$\displaystyle{\left({A}=\pi{\left({2.6}\right)}^{{{2}}}\right)}$$ of the solenoid
$$\displaystyle{L}=\mu_{{{0}}}{\frac{{{N}^{{{2}}}}}{{{l}}}}{A}$$
substituting the values we can find N
on solving, we get $$N = 38$$ turns