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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:
Options
case (i) contradicts Gauss’s law for electrostatic fields.
case (ii) contradicts Gauss’s law for magnetic fields.
case (i) agrees with `oint E.dl = 0`
case (ii) contradicts `oint H.dl = I_(en)`
Solution
case (ii) contradicts Gauss’s law for magnetic fields.
Explanation:
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 Gauss's law of electrostatic field `oint_s E.ds = q/ε_0`. 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_s B.ds = 0`. It contradicts for magnetic field, because there is magnetic field inside the solenoid and no field outside the solenoid marrying current, but the magnetic field lines from the closed paths.
This implies that number of magnetic field lines entering the Gaussian surface is equal to the number of magnetic field lines leaving it.
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