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Magnetism And Matter — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsMagnetism And Matter1 Mark
MCQ
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:
  • 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 $\oint\text{E.dl=0.}$
  • D
    Case (ii) contradict $\oint\text{H.dl}=\text{I}_\text{en}$.
✓

Answer

  1. 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, $\oint\text{E.ds}=\frac{\text{q}}{\in_0}$ 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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