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) $\overrightarrow{E}$ 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 given.

• A. Case (i) contradicts Gauss's law for electrostatic fields
• B. Case (ii) contradicts Gauss's law for magnetic fields
• C. Case (i) agree with $\oint \overrightarrow{E}\cdot \overrightarrow{dl}=0$
• D. Case (ii) contradicts $\oint \overrightarrow{H}\cdot \overrightarrow{dl}=I_{en}$

Answer 1

The correct option is B Case (ii) contradicts Gauss's law for magnetic fields

We know that the Electric field lines do not form a closed loop whereas the magnetic field lines form constant closed loop.

The Gauss' law for electrostatics states that:

$\int E.dl=\frac{Q}{{\epsilon }_0}$

And the Gauss' law for magnetic field states that:

$\int B.ds=0$

It means that the number of the magnetic field lines entering the closed surface is same as the number of lines exiting the surface. this contradicts the second case.

Option $\left(B\right)$ is correct.