MCQ
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$, radius of 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.
  • Case $(ii)$ contradicts Gauss’s law for magnetic fields.
  • C
    Case $(i)$ agrees with $\oint\text{E.dl=0.}$
  • D
    Case $(ii)$ contradict $\oint\text{H.dl}=\text{I}_\text{en}$.

Answer

Correct option: B.
Case $(ii)$ contradicts Gauss’s law for magnetic fields.

Key concept: The electrostatic field lines, do not form a continuous closed path (this follows from the conservative nature of electric field) while the magnetic field lines form the closed paths.
According to the Gauss' law, $\oint\text{E.ds}=\frac{\text{q}}{\in_0}$ for electronstatic field. It does not contradict foe eletrostatic fields as the elecric field lines do not form a continuous closed path.
According to Gauss' law in magnetism.
$\oint\text{B.ds}=0$
Which implies that number of magnetic field lines entering the Gaussian surface is equal to the number of magnetic field lines leaving it. Therefore case $(ii)$ is not possible.

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