Consider the two idealized systems: (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length `Lgt gt R`, radius of cross-section. In (i) `vecE` 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 law as below:

Options

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 `vecE.vecdl = 0 `
D. case (ii) contradicts` oint vecH .vec dl = I_("en")`

Answer

B

Explanation

According to Gauss.s law of magnetism, `oint vecB d vecA =mu_0 I` , which implies that magnetic field side the solenoid is non-zero but here it is given to be zero. So, case (ii) contradicts Gauss.s law for magnetic fields. On the other hand, electric field lines do not form closed loops.
According to Gauss.s law of electrostatic fields, `oint vecE d vecA = (Q)/(epsi_0) ` . Since, the total charge on two plates of capacitors is zero, therefore, `oint vecEd vecA = 0` . So, case (i) agrees with the Gauss.s law of electrostatic fields. Also, electric field lines do not form closed loops, so option (c) is incorrect. On the other hand, magnetic field lines always form closed loops, so option (d) also is incorrect.