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Conductors, insulators, dielectrics and polarization: NEET MCQs with answers

50 questions on this topic of Electrostatics (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. Which of the following substances behaves as an insulator at room temperature but can show significant electrical conductivity when subjected to an electric field exceeding its dielectric breakdown strength?

  1. Copper
  2. Mercury
  3. Silver
  4. Fused quartz
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Answer: (D) Fused quartz

Fused quartz is an excellent dielectric insulator under normal conditions. When an external electric field exceeds its dielectric strength, dielectric breakdown occurs, ionizing the atoms and allowing it to conduct electricity. Metals like copper, silver, and mercury are natural conductors at room temperature.

medium

2. A neutral metallic sphere of radius R has a spherical cavity of radius r at its center. A point charge +q is fixed at the center of the cavity. What is the electric potential at a distance d from the center, where r < d < R?

  1. q / (4πε₀) · [1/d - 1/R]
  2. q / (4πε₀d)
  3. zero
  4. q / (4πε₀R)
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Answer: (D) q / (4πε₀R)

The metal body occupies the region r ≤ x ≤ R. Inside a conductor in electrostatic equilibrium, the electric field is zero, meaning the entire conductor is equipotential. The potential of the conductor is determined by the total enclosed charge appearing on its outer surface of radius R, which is V = q / (4πε₀R).

hard

3. A solid conducting sphere of radius R carries a net charge +Q. It is surrounded by a concentric uncharged spherical conducting shell of inner radius 2R and outer radius 3R. The electrostatic potential of the inner conducting sphere is:

  1. Q / (6πε₀R)
  2. 5Q / (12πε₀R)
  3. 5Q / (24πε₀R)
  4. Q / (4πε₀R)
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Answer: (C) 5Q / (24πε₀R)

The charge +Q on the inner sphere induces -Q on the inner surface of the shell (at r = 2R) and +Q on the outer surface of the shell (at r = 3R). The potential of the inner sphere is the sum of potentials due to all three spherical charge distributions: V = (1/4πε₀) [ Q/R - Q/(2R) + Q/(3R) ] = (Q/4πε₀R) [ 1 - 1/2 + 1/3 ] = (5/6) × [ Q / (4πε₀R) ] = 5Q / (24πε₀R).

medium

4. Consider the following two statements: Statement I: When a neutral conductor is placed in an external electrostatic field, the induced surface charges produce an internal field that completely cancels the external field inside the conductor. Statement II: In a dielectric, induced charges produce an internal field that is greater than the external field, reversing the direction of the net electric field.

  1. Both Statement I and Statement II are correct.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. Both Statement I and Statement II are incorrect.
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Answer: (B) Statement I is correct but Statement II is incorrect.

Statement I is correct because free electrons move until the internal induced field exactly cancels the external field, giving E_net = 0. Statement II is incorrect because bound charges in a dielectric only partially oppose the external field, so the net field is reduced by a factor K (E = E₀/K) but remains in the same direction as E₀.

easy

5. The mechanical force per unit area acting on the surface of a charged conductor in electrostatic equilibrium with surface charge density σ in vacuum is given by:

  1. σ² / (2ε₀) directed tangentially along the surface
  2. σ² / ε₀ directed normally outward
  3. σ² / (2ε₀) directed normally outward
  4. σ / (2ε₀) directed normally inward
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Answer: (C) σ² / (2ε₀) directed normally outward

The outward electrostatic pressure on a charged conductor is P = σ² / (2ε₀). It is always directed normally outward from the surface, regardless of the sign of the charge, because like charges on adjacent surface elements repel each other.

hard

6. A spherical conductor of radius a has a charge Q. It is connected by a thin conducting wire to another uncharged spherical conductor of radius b (b ≠ a) kept far apart. After electrostatic equilibrium is reached, the ratio of the surface charge density on sphere a to that on sphere b (σₐ / σᵦ) is:

  1. a / b
  2. b / a
  3. b² / a²
  4. a² / b²
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Answer: (B) b / a

When connected by a wire, the conductors reach the same potential: Vₐ = Vᵦ, so Qₐ / (4πε₀a) = Qᵦ / (4πε₀b), which yields Qₐ / Qᵦ = a / b. The surface charge densities are σₐ = Qₐ / (4πa²) and σᵦ = Qᵦ / (4πb²). Therefore, σₐ / σᵦ = (Qₐ / Qᵦ) × (b² / a²) = (a / b) × (b² / a²) = b / a.

easy

7. A solid conducting sphere of radius R carries a net charge Q. What is the electrostatic potential at the center of the sphere?

  1. Zero
  2. Infinite
  3. Q / (8πε₀R)
  4. Q / (4πε₀R)
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Answer: (D) Q / (4πε₀R)

Inside a conductor in electrostatic equilibrium, the electric field is zero everywhere. Thus, the electric potential is constant throughout the entire volume of the conductor and equal to its value on the surface, which is V = Q / (4πε₀R).

easy

8. Which of the following molecules has a permanent electric dipole moment even in the absence of an external electric field?

  1. Water (H₂O)
  2. Methane (CH₄)
  3. Carbon dioxide (CO₂)
  4. Nitrogen (N₂)
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Answer: (A) Water (H₂O)

H₂O has a bent or V-shaped geometry due to the two lone pairs on oxygen, causing the individual O-H bond dipole moments to add vectorially to yield a non-zero permanent dipole moment. CO₂, CH₄, and N₂ have symmetric structures where the centers of positive and negative charges coincide, giving zero permanent dipole moment.

easy

9. A solid conducting sphere of radius R carries a net positive charge Q. At a point located at a distance r (where r < R) from the center of the sphere, the electrostatic potential is:

  1. Constant and equal to Q / (4πε₀R)
  2. Directly proportional to r
  3. Inversely proportional to r
  4. Zero
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Answer: (A) Constant and equal to Q / (4πε₀R)

Inside a conductor in electrostatic equilibrium, the electric field is zero everywhere. Since E = -dV/dr, the electric potential remains constant throughout the volume of the conductor and is equal to its value at the surface, which is Q / (4πε₀R).

medium

10. Molecules such as H₂O, which have a permanent dipole moment even without an external field, are called:

  1. Conductors
  2. Superconductors
  3. Polar molecules
  4. Non-polar molecules
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Answer: (C) Polar molecules

In polar molecules the centres of positive and negative charge do not coincide, giving a permanent dipole moment. In non-polar molecules (e.g. O₂) they coincide.

NCERT Class 12

easy

11. A linear isotropic dielectric material is placed in an external electric field E₀. If the induced bound surface charge density produces an internal polarization field Eₚ that opposes E₀, the dielectric constant K of the material in terms of E₀ and the net electric field E inside the dielectric is given by:

  1. E / E₀
  2. (E₀ - E) / E₀
  3. E₀ / E
  4. (E₀ + E) / E
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Answer: (C) E₀ / E

Inside a dielectric, the net reduced electric field is E = E₀ - Eₚ. By definition of the dielectric constant (relative permittivity), K = E₀ / E.

medium

12. A dielectric slab with dielectric constant K = 2.5 is placed between the plates of a parallel plate capacitor. Inside the dielectric, the net electric field is measured to be 4.0 × 10⁵ V m⁻¹. What is the magnitude of the electric field produced solely by the induced bound surface charges (E_ind)?

  1. 1.0 × 10⁶ V m⁻¹
  2. 2.4 × 10⁵ V m⁻¹
  3. 6.0 × 10⁵ V m⁻¹
  4. 1.6 × 10⁵ V m⁻¹
Show answer and explanation

Answer: (C) 6.0 × 10⁵ V m⁻¹

The applied external field is E₀ = K × E = 2.5 × (4.0 × 10⁵ V m⁻¹) = 1.0 × 10⁶ V m⁻¹. The field produced solely by the induced bound charges opposes the external field, so E_ind = E₀ - E = 1.0 × 10⁶ - 4.0 × 10⁵ = 6.0 × 10⁵ V m⁻¹.

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