Consider the two idealized systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L>>R, the radius of the cross-section. In (i) E is ideally treated as a constant between plates and zero outside. In (ii) the magnetic field is constant inside the solenoid and zero outside. These idealized assumptions, however, contradict fundamental laws as below:

1. case (i) contradicts Gauss' law for electrostatic fields
2. case (ii) contradicts Gauss' law for magnetic fields
3. case (i) agrees with $\oint E.dl=0$
4. case (ii) contradicts $\oint H\cdot dI={I}_{en}$

(b) Hint: Use Gauss law for the electric field as well as for the magnetic field.
Step 1: As Gauss' law states, ${\oint }_{S}E\cdot ds=\frac{q}{{\epsilon }_{0}}$ for the electrostatic field. It does not contradict electrostatic fields as the electric field lines do not form a continuous closed path.
Step 2: According to Gauss' law in the magnetic field,
$\oint E\cdot ds=0$
It contradicts for the 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.