Question

Calculate the inductance of the inductive sensor detecting a Carbon steel bar. (The Bar has an end on area of r x r )

μ₀=4πx10^-7H/m

n=63turns

t=3mm

r=2mm

d=2mm

R=36m

P=36m

µ_c IRON = 5000

µ_A Carbon steel = 100

Note: The core is not a semicircle you need to calculate the Reluctance due to the path length

permeability HA Air gap a R P ለ ለለ

Answer 1

Solution:

The inductance of the inductive sensor detecting a Carbon steel bar is calculated.

are: n = 63 turns raamm • Rivont esteedt Rair gap Solution Given values do= 4x1074/os ta 3mm d=2mm R=36m p=36m MC IRON & permeability of iron} = 5,000 MA Carbon Steel & permeability of carbon steed= 1,00 Although formula for inductance is given by, na . Riotal where しっ CS Scanned with CamScanner

Rixon= Iiron MoMe Airon . Iiron PtartP Airon TOR Q TR2= TE2 .. Riron CP+ 28+P) MoMe (TT+2) 1 1 1 substituting these values, Rirona (36m +2(367) +36m) 4TX 107 X5000 XTXBxrömma Riton = 8-105X108 AT/Wb Rsteel Isteel MOMA Asteel .. Isteel = QR Asteel Td? = (2x1072) = TEX 1060 2 4 cs Scanned with CamScanner

& Rsteel a Car) MOMA ( (10) ..Rsteels 2136) 47TX 107 X 100 X TTX10-6 1823.78 x108 AT/Wb Rain l gap= MA ad ATTX 107 XA A= 975 X 10-6 ma Rair gap- QXQX10-3m ATTX 10 7x 9TX10 = 1.125 X10* AT Wb CS Scanned with CamScanner

Perotal = Riront Rsteel thair gap Incluctance .L= na .H R Total (8.105 + 1823.78 + 1.125) x1 1.125) x108 A7 Wb =1833.01 X108 AFWb La (63)2 1833.01X108 AT/Wh La 0.00000002165 L=0.02165 MH CS Scanned with CamScanner