Consider the two idealized systems: (i) a parallel plate

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) magnetic field is constant inside the solenoid and zero outside.

These idealised assumptions, however, contradict fundamental laws as below:

(a) case (i) contradicts Gauss’s law for electrostatic fields

(b) case (ii) contradicts Gauss’s law for magnetic fields

(c) case (i) agrees with

$\oint E . d l=0$

(d) case (ii) contradicts

$\oint H . d l=I_{e m}$