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(C) According to Faraday's law of induction,the induced $emf$ in a loop is given by $\varepsilon = |\frac{d\phi}{dt}|$,where $\phi = B \cdot A$ is the

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$\varepsilon$

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(C) According to Faraday's law of induction,the induced $emf$ in a loop is given by $\varepsilon = |\frac{d\phi}{dt}|$,where $\phi = B \cdot A$ is the magnetic flux.Since the magnetic field $B$ is confined to a region of radius $a$,the magnetic flux through any loop with radius $r \ge a$ is $\phi = B \cdot (\pi a^2)$.The induced $emf$ is $\varepsilon = \frac{d}{dt}(B \pi a^2) = \pi a^2 \frac{dB}{dt}$.Note that the induced $emf$ depends only on the area of the region where the magnetic field exists,not on the radius of the wire loop,provided the loop encloses the entire magnetic field region.Since both loops (of radius $b$ and $2b$) enclose the entire region of radius $a$,the magnetic flux through both loops is the same.Therefore,the induced $emf$ in the loop of radius $2b$ is the same as the induced $emf$ in the loop of radius $b$,which is $\varepsilon$.

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