An electromagnet is used to support a solid pieceof steel.Aforce of 10,000 N is required to support the weight. The cross-sectional area of the magnetic core (the fixed part) is 0.01 m2.The coil has 1,000 turns. Determine the minimumcurrent that can keep the weight from falling forx = 1.0 mm. Assume negligible reluctance for the steelparts and negligible fringing in the air gaps.

University Physics Volume 2
18th Edition
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Author:OpenStax
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Chapter13: Electromagnetic Induction
Section: Chapter Questions
Problem 30P: A long solenoid with n= 10 turns per centimeter has a cross-sectional area of 5.0 cm2and carries a...
Question

An electromagnet is used to support a solid piece
of steel.Aforce of 10,000 N is required to support the weight. The cross-sectional area of the magnetic core (the fixed part) is 0.01 m2.
The coil has 1,000 turns. Determine the minimum
current that can keep the weight from falling for
x = 1.0 mm. Assume negligible reluctance for the steel
parts and negligible fringing in the air gaps.

Expert Solution
Step 1

Given Data:

The force required to support the weight is, F=10,000 N

The cross-sectional area of the magnetic force is, A=0.01 m2

The number of turns on the coil is, N=1000

The displacement is, x=1.0 mm

 

The expression for the current for a force to require the support is,

Physics homework question answer, step 1, image 1

Here, ϕ is the magnetic flux, and Rgap is the variable reluctance of the air gap.

The variable reluctance of the air gap is calculated as,

Physics homework question answer, step 1, image 2

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