GATE 2021 PH – Question 63
The electromagnet shown has a 5 cm air gap and a core of magnetic permeability $\mu=20000\mu_0$. It is driven by a coil with $NI=10^4$ A-turns. Core cross-section dimensions and outer dimensions are shown. Ignoring fringing fields, find the gap magnetic flux density $B$ in tesla, rounded to two decimal places.
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Correct answer: .24 to .26
Explanation
The core has uniform 3 cm thickness. Its mean rectangular path dimensions are $9-3=6$ cm and $17-3=14$ cm. Thus the mean iron length is $2(6+14)-5=35$ cm, after subtracting the air gap. Ampère’s law gives $NI=B l_g/\mu_0+B l_c/(20000\mu_0)$. Therefore $B=\mu_0NI/(0.05+0.35/20000)=0.25124$ T, which rounds to 0.25 T.