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  • 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, the radius of the cross-section.

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, the radius of the cross-section.

In (i) E is ideally treated as a constant between plates and zero outside.
In (ii) the 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) agrees with \int E.dl=0
D. case (ii) contradicts \int H.dl=l_{en}

 

Answers (1)

The answer is the option (b)
Gauss’ Law for electrostatic field isn’t violated as electric fields don’t require to be in continuous closed paths.
\oint_{}S E.ds=\frac{q}{\varepsilon_ 0}
However, Gauss’ Law for magnetic field is violated as magnetic fields need to be in continuous closed paths.
\oint_{}S B.ds=0

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