Consider the two idealized systems: (i) a parallel plate capacito… - Vidyadip

Question

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:

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Answer

Case (ii) contradicts Gauss’s law for magnetic fields.

Solution:
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, $\oint\text{E.ds}=\frac{\text{q}}{\epsilon_0}$ 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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