Ou high-school professor told us that a time varying magnetic field in a cylindrical region produces a sort of circular electric field which is Non conservative in nature, because Electric field varies radially, however, I fail to understand why that is the case.
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$\begingroup$ Faraday's law $\endgroup$– FarcherCommented Aug 27, 2023 at 8:50
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Consider the region outside a cylindrical tube of magnetic flux that varies in time, $\Phi(t)$. Faraday's law tells you the closed line integral of the E-field is (minus) the rate of change of magnetic flux enclosed. The line integral is the E-field (which will circulate around the tube in the $\hat{\phi}$ direction) multiplied by $2\pi R$. $$\oint \vec{E}\cdot d\vec{l} = 2\pi R E_\phi = -\frac{d\Phi}{dt}\ .$$ Thus, rearranging we have an E-field that falls as $R^{-1}$.
Why is this non-conservative? Well, because the closed line integral around the tube is non-zero.
If you want to consider the E-field within the flux tube then you need to specify how the B-field varies with $R$. If it were uniform then the enclosed flux on the right hand side of Faraday's law varies as $R^2$ and the induced E-field varies as $R$. In any case you cannot make the right hand zero if the enclosed flux varies with time, so the E-field will always be non-conservative.
