is the number of field lines depends on dielectric constant of a medium
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Dielectric Constant, also called relative permitivity of a medium depends on the electric susceptibility of it, the ease with electric flux lines can pass through it. The susceptibility depend on molecular polarization, the electric dipole moment acquired per unit volume in an external electric field. So, the thing to note is that, dielectric constant is a physical quantity measured as a comparison of the strength of electric field in vacuum to that inside the material.
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