Case: Read the passage and answer the question.
Conductors contain mobile charge carriers. In metallic conductors, these charge carriers are electrons. In a metal, the outer (valence) electrons part away from their atoms and are free to move. These electrons are free within the metal but not free to leave the metal. The free electrons form a kind of ‘gas’; they collide with each other and with the ions and move randomly in different directions. In an external electric field, they drift against the direction of the field. The positive ions made up of the nuclei and the bound electrons remain held in their fixed positions. A dielectric (an insulator) behaves differently. Its charges are held to their atoms or molecules and cannot move freely through it. An external electric field can only shift these charges a little or turn the molecules. The dielectric is then said to be polarised.
An uncharged metal slab and a dielectric slab of dielectric constant 4 are placed in the same uniform external electric field \( E_0 \). The faces of both slabs are normal to the field. What is the net electric field inside each slab in the static situation?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Zero inside the metal slab; \( E_0/4 \) inside the dielectric slab
Both slabs get induced charges on their faces. The field of these charges acts against the external field inside the slab. In a metal the net field inside becomes zero. In a dielectric of dielectric constant \( K \) it only reduces the field, to \( E_0/K \).
Option (1) Zero inside the metal slab; \( E_0/4 \) inside the dielectric slab — Correct. The free electrons of the metal keep moving until the net field inside is zero. In the dielectric, the bound charges on the faces have a smaller density, \( \sigma-\sigma_p=\sigma/K \). So the field inside is \( E_0/K=E_0/4 \).
Option (2) Zero inside both slabs — Incorrect. The charges of a dielectric are bound to its molecules and cannot move through the slab. So the field inside it is reduced but does not become zero.
Option (3) \( E_0/4 \) inside the metal slab; zero inside the dielectric slab — Incorrect. The two slabs are swapped here. A metal cannot keep any field inside it in the static situation, while a dielectric keeps a part of the field.
Option (4) Zero inside the metal slab; \( 4E_0 \) inside the dielectric slab — Incorrect. The field of the induced charges opposes the external field. So the field inside the dielectric becomes smaller, \( E_0/K \). It does not grow to \( KE_0 \).
NCERT (2026-27):
Dielectrics and Polarisation – “The free charge carriers move and charge distribution in the conductor adjusts itself in such a way that the electric field due to induced charges opposes the external field within the conductor. This happens until, in the static situation, the two fields cancel each other and the net electrostatic field in the conductor is zero. In a dielectric, this free movement of charges is not possible. … Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field. It only reduces it.”
Effect of Dielectric on Capacitance – “The electric field in the dielectric then corresponds to the case when the net surface charge density on the plates is ±(σ – σp). That is,”
\( \displaystyle E=\frac{\sigma-\sigma_P}{\varepsilon_0} \qquad (2.47) \)
“… Thus, (σ – σp) is proportional to σ and we can write”
\( \displaystyle \sigma-\sigma_P=\frac{\sigma}{K} \)\( \qquad (2.49) \)