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(B) Given that the magnetic flux is increasing out of the page,by Lenz's law,an induced electric field is created in the clockwise direction. The emf

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$-\varepsilon_{0}, 0$

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(B) Given that the magnetic flux is increasing out of the page,by Lenz's law,an induced electric field is created in the clockwise direction. The emf around the loop is $\oint E \cdot ds = \varepsilon_{0}$.For path $1$,which encloses the solenoid,the line integral of the electric field from $a$ to $b$ is $\int_{a}^{b} E \cdot ds = \varepsilon_{0}$. Therefore,$V_{b}-V_{a} = -\int_{a}^{b} E \cdot ds = -\varepsilon_{0}$.For path $2$,which does not enclose the solenoid,the magnetic flux enclosed is zero. Thus,the line integral of the induced electric field along this path is zero,meaning $\int_{a}^{b} E \cdot ds = 0$. Therefore,$V_{a}-V_{b} = -\int_{b}^{a} E \cdot ds = 0$.

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