Question: Q. 2. Consider the two idealized systems : (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length $L \gg R$, 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 idealized 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) agreeswith $\oint_{s} E . d l=0$
(d) case (ii) contradicts $\oint H \cdot d l=I_{e n}$
Show Answer
Solution:
Ans. Corred option : (b)
Explanation: According to Gauss’s law of
electrostatic field,
$$ \oint E . d s=\frac{q}{\varepsilon_{0}} $$
[NCERT Exemplar]
So it does not contradict for electrostatic field as the electric field lines do not form continuous path.
According to Gauss’s law of magnetic field,
$$ \oint B \cdot d s=0 $$
It is clear that it contradicts for magnetic field because there is magnetic field inside the solenoid, and no field outside the solenoid carrying current, but the magnetic field lines form the closed paths.
