GATE 2015 EE – Question 21
Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is $0.4\ \Omega$, and its inductance is negligible. The magnetic flux density (in Tesla) as a function of time, and is given by $B(t) = 0.25\sin\omega t$, where $\omega = 2\pi \times 50$ radian/second. The power absorbed (in Watt) by the loop from the magnetic field is ________.
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Correct answer: 0.17 to 0.2
Explanation
The loop area is $0.1 \times 0.05 = 0.005$ m$^2$. By Faraday's law the peak emf is $A \times 0.25 \times \omega = 0.005 \times 0.25 \times 314.16 = 0.3927$ V, so the rms emf is $\frac{0.3927}{\sqrt{2}} = 0.2777$ V. The power in the $0.4\ \Omega$ loop is $\frac{0.2777^2}{0.4} = 0.193$ W.