JEE Main Physics: Field due to uniformly charged infinite plane sheet Practice Questions

Correct answer: B — 0

The field due to +σ is E₁ = σ/2ε₀ (pointing away from the positive sheet). The field due to -σ is E₂ = (-σ)/2ε₀ (pointing towards the negative sheet). Since the sheets are identical and parallel, the fields cancel out: Eₙₑₜ = E₁ + E₂ = 0.

Correct answer: D — Varies linearly with the distance from the sheet

The electric potential V due to an infinite plane sheet is constant everywhere, meaning it does not depend on the distance from the sheet, although the potential itself is not zero unless reference is taken at infinity.

Correct answer: A — It is doubled

Since E = σ/ (2ε₀), if σ is doubled, the electric field E is also doubled.

Correct answer: D — Perpendicular to the sheet, pointing away from the sheet

The electric field due to an infinite plane sheet is always perpendicular to the plane of the sheet. If the sheet has a positive charge, the field points away from the sheet (or towards it if the sheet is negative).

Correct answer: D — σ/ (2ε₀)

The electric field due to an infinite plane sheet is E = σ/ ε₀.

Correct answer: D — 0

Since the electric field is directly proportional to the surface charge density (σ), if σ=0, the resulting electric field is zero.

Correct answer: B — σ/ ε₀

The magnitude of the electric field (E) produced by an infinite plane sheet of charge density σ is E = σ/ ε₀, where ε₀ is the permittivity of free space.

Correct answer: A — The field is proportional to σ and is independent of the distance.

The electric field is directly proportional to the surface charge density (E⃗ = σ/ (2ε₀)), and for an infinite sheet, the field magnitude depends only on σ and not on the point of observation location, provided the observation point is perpendicular to the sheet.

Correct answer: C — The surface charge density of the sheet

The formula for the electric field is E = σ/ ε₀. Since ε₀ is a constant, the field E is directly proportional to the surface charge density σ.

Correct answer: B — Perpendicular to the sheet, pointing away from the sheet

The electric field lines of a uniformly charged infinite plane sheet are perpendicular to the sheet and point away from the sheet (if σ is positive).

Correct answer: A — σ/ (2ε₀ z)

The electric potential V created by an infinite plane sheet is V = -σ/2ε₀ z. Since the question asks for proportionality, V ∝ z is incorrect for an infinite sheet; potential is linear with distance. The potential decreases linearly with distance from the sheet.

Correct answer: D — σ/(2ε₀ r)

The electric field produced by an infinite plane sheet of charge density σ is E = σ/ (2ε₀), which is constant everywhere perpendicular to the sheet and independent of the distance r. If we consider the field magnitude per unit length, it is σ/ (2ε₀) in the direction perpendicular to the sheet. When calculating the magnitude of the field at a distance r, the formula is simplified in the context of an infinite sheet where the field magnitude is σ/ (2ε₀) regardless of r. However, the standard derivation for the field magnitude from a sheet is E = σ/ (2ε₀).

Correct answer: C — It is doubled.

Since the electric field E is directly proportional to the surface charge density σ (E = σ/ ε₀), doubling σ will double the electric field magnitude.

Correct answer: C — Zero

The electric field produced by an infinite plane sheet is constant and perpendicular to the sheet. If the charges are equal and opposite, the fields cancel out at the midpoint. The field on one side is E = σ/ε₀, and the field on the other side is E = -σ/ε₀ (or magnitude σ/ε₀). Thus, the net field at the midpoint is zero.

Correct answer: B — σ/ ε₀

For an infinite plane sheet, the electric field is uniform and given by E = σ/ ε₀, regardless of the distance d. The distance d does not appear in the final expression for the field magnitude.