When magnetic flux is changed linked with the coil the the electric field is produced inside the coil. But this electric field is non-conservative field whereas the electric field produced by the static charge is conservative. Why when the magnetic flux is changed linked with the coil electric field induced is nonconservative? Why a static charge produce conservative Field?
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For a vector field to be conservative (in this case, the vector field will be your electric field), you want the circulation around any closed loop to be $0$. Mathematically, you want $$\oint_{\mathcal{C}} \mathbf{E} \cdot \mathrm{d}\mathbf{r} = 0$$ for any closed loop $\mathcal{C}$.
Faraday's law states the following for an electric field generated by a changing magnetic flux: $$\oint_{\mathcal{C}} \mathbf{E} \cdot \mathrm{d}\mathbf{r} = -\frac{\partial \Phi_B}{\partial t}$$
where $\Phi_B$ is the magnetic flux through the region bounded by $\mathcal{C}$. As you can see, in the presence of a changing magnetic flux, the circulation of your electric field will be non-zero. I.e., the electric field generated by the changing magnetic flux is non-conservative.
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