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) $\vec{E}$ 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 $\oint \vec{E}\cdot \overrightarrow{dl}=0$
• D. case (ii) contradicts $\oint \vec{H}\cdot \overrightarrow{dl}=I_{en}$

Answer 1

Answer: (B)

According to Gauss’s law in magnetism $\oint \vec{B}\cdot \overrightarrow{dS}=0$, 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.