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 idealized assumptions, however, contradict fundamental laws as below:

Question

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 idealized assumptions, however, contradict fundamental laws as below:

Philoid · Accepted Answer

_{As the first scenario says that E is treated as a constant and zero outside, the plate is true. If the plates are taken of infinite length and the distance is very small like very, very small only then the electric field E is taken as constant between the parallel plates and due to opposite and equal charges zero outside the plate hence no contradiction.}

_{Whereas in the second case according to the Gaussian law the magnetic field is defined in terms of permeability and current flowing in the object by the relation}

where

is the magnetic fieldis the lengthis the permeability andis the current flowing.

The current flowing is non-zero for a solenoid as the number of magnetic lines entering the solenoid is same as that of leaving therefore, the second statement is wrong.