Consider the two idealised systems $(i)$ a parallel plate capacitor with large plates and small separation and $(ii)$ a long solenoid of length $L >> R$, radius of cross-section. In $(i)\, E$ ideally treated as a constant between plates and zero outside. In $(ii)$ magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below
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As Gauss' law states,$\oint\limits_s {E.dS} = \frac{q}{{{\varepsilon _0}}}$ electrostatic field. It does not contradict for electrostatic fields as the electric field lines do not form continuous closed path. According to Gauss' law in magnetic field, $\oint\limits_s {E.dS} = 0$ It contradicts for magnetic field, because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.
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