Question

Consider the two idealised 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’ law for electrostatic fields(b) case (ii) contradicts Gauss’ law for magnetic fields(c) case (i) agrees with $\oint E.dl=0$.(d) case (ii) contradicts $\oint H.dl=I_{en}$

Answer 1

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Quetion :- Consider the two idealised 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

Answer :- case (ii) contradicts Gauss’ law for magnetic fields

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Answer 2

Answer:

Explanation:

According to the Gauss's law for electrostatic field. ie = ФE.ds = q/e0.

It does not contradict for an electrostatic field as the electric field lines do not form a continuous closed path.

According to Gauss's law in magnetic field, ie ФB.ds = 0  

It contradicts for the magnetic field because there is a magnetic field inside the solenoid. There is no field outside the solenoid carrying current but still the magnetic field lines form the closed paths.

Hence, this implies that the 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