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(D) The radius of the loop grows linearly with time,so $r(t) = kt$,where $k$ is a constant.The magnetic field is given by $B(r) = \frac{C}{r}$ for som

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$E$ is constant

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(D) The radius of the loop grows linearly with time,so $r(t) = kt$,where $k$ is a constant.The magnetic field is given by $B(r) = \frac{C}{r}$ for some constant $C$.The magnetic flux $\phi$ through the loop is calculated by integrating over the area: $\phi = \int B(r) dA = \int_{0}^{r} \left(\frac{C}{r'}\right) (2\pi r' dr') = \int_{0}^{r} 2\pi C dr' = 2\pi C r$.Substituting $r = kt$,we get $\phi = 2\pi C (kt) = (2\pi C k) t$.The induced emf $E$ is given by Faraday's Law: $E = -\frac{d\phi}{dt}$.$E = -\frac{d}{dt} [(2\pi C k) t] = -2\pi C k$.Since $C$ and $k$ are constants,the emf $E$ is constant.

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