GATE 2016 EE (EE2) – Question 52

Electrical Machines · Auto-transformer, Electromechanical energy conversion principles · 2 marks · Numerical answer

An electromagnetic system has flux linkage $\lambda=\sqrt i/g$. For i=2 A and air gap g=10 cm, the mechanical-force magnitude in newtons is ________.

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Correct answer: 186.0 to 190.0

Explanation

For prescribed current, force is the gap derivative of magnetic coenergy. Integrate linkage over current: $W\prime(i,g)=\int_0^i\sqrt{\iota}/g\,d\iota=2i^{3/2}/(3g)$.

Differentiating with respect to g gives a negative force tending to close the gap. Its magnitude is $2i^{3/2}/(3g^2)$.

At i=2 and g=0.1 m, this is **188.562 N**, within 186–190 N.

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