Calculate the inductance of a closely wound solenoid of length l whose winding is made of copper wire of mass m. The winding resistance is equal to R. The solenoid diameter is considerably less then its length. Given, density of copper = d and resistivity = ρ
Text Solution
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Sol. Let the radius of solenoid be a, total number of turns N and let cross-sectional area of wire be S.
Then length of the wire of which the solenoid is made = 2 π aN
But its resistance is R
∴ R = ρ 
or aN = 
….. (1)
Mass of the wire is given as m
∴ (2 p aN) Sd = m
or aN = 
….. (2)
From equations (1) and (2)
(aN) 2 = 
….. (3)
Self-Inductance of a solenoid is L = 
where A = π a 2 ∴ L = 
= 
or L = 
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