An air-core solenoid having a diameter of 4cm and of length 60cm is wound with 4000 turns. find the inductance of the solenoid. what will be the inductance of the solenoid if it has an iron core of relative permeability of 4000 ?
Answers
Explanation:
L = (PERMEABILITY OF FREE SPACE X RELATIVE PERMEABILITY X NO.OF TURNS² X AREA)/L
=( 8.854 X 10^-12. X 4000 X 4000² X π X 2² )/60
Given info : An air-core solenoid having a diameter of 4cm and of length 60cm is wound with 4000 turns. it has an iron core of relative permeability of 4000.
To find :
- find inductance of solenoid
- find inductance of solenoid when it has an iron of relative permeability of 4000.
solution : inductance of solenoid, L = μ₀N² × area/length
= 4π × 10^-7 × (4000)² × {π × (2 × 10¯² m)²}/{0.6m}
= 4π × 10^-7 × 16 × 10^6 × π × 4 × 10¯⁴/0.6
= 0.0421 H
now inductance of solenoid when it has an iron core of relative permeability is 4000, L' = μ_r L
= 4000 × 0.042 H
= 168.4 H
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