A non-uniform magnetic field B exists in a cylindrical region of radius 0.5m as shown. A uniform conducting wire of length 8m and total resistance 4Ω is bent into a square frame and is placed with one

Question

A non-uniform magnetic field B exists in a cylindrical region of radius 0.5m as shown. A uniform conducting wire of length 8m and total resistance $4Ω$ is bent into a square frame and is placed with one side along the diameter of cylinder as shown. If $\frac{dB}{dt} = 1 Tesla / sec$ , find current induced in frame (in mA) (Rounded off to $2^{nd}$ decimal place) $____$ . (Take : $π = 3.14$ )

TestHub · Accepted Answer

Only the semicircular part of the frame lies inside the cylindrical field region, so the flux through the frame: $ϕ = \frac{B π R ^{2}}{2}$

EMF induced: $E = \frac{π R ^{2}}{2} \frac{d B}{d t} = \frac{π}{2} (\frac{1}{2})^{2} (1) = \frac{π}{8} volt$

Current: $I = \frac{E}{4} = \frac{π}{32} A = \frac{3.14}{32} A = 98.12 mA$

Answer: 98.10 to 98.20

Physics - EMI/AC Question with Solution | TestHub

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