Physics · Electric Charges And Fields · NEET
They differ only in what you divide the charge by. λ (linear) = ΔQ/Δl divides charge by length, so it is used for a thin wire or ring (unit C/m). σ (surface) = ΔQ/ΔS divides charge by area, used for a sheet, plate, or the surface of a shell (unit C/m²). ρ (volume) = ΔQ/ΔV divides charge by volume, used for charge spread through a solid body (unit C/m³). First ask: is the charge on a line, a surface, or through a volume? That choice fixes which symbol you use.
Match the density to the shape given in the question. A charged wire, rod, or circular ring uses λ. A charged flat sheet, a disc, or the outer surface of a conductor or shell uses σ. A charged solid sphere or a cloud of charge filling a volume uses ρ. NEET Gauss's law problems tell you the shape, so pick the density that matches that shape.
You multiply the density by the correct amount of length, area, or volume. If the density is uniform: Q = λ × L for a wire of length L, Q = σ × A for a surface of area A, and Q = ρ × V for a solid of volume V. For example a sphere of surface area 4πR² with density σ carries Q = σ × 4πR². If the density is not uniform you integrate (add up small pieces), but NEET almost always uses uniform density.
A charge of just 1 microcoulomb already contains about 10¹³ electrons. Counting each electron is impossible and pointless. So we treat the charge as a smooth, continuous fluid and describe it with a density, exactly like we treat water as a continuous fluid with a mass density instead of counting molecules. This makes the field calculation practical.
λ, σ and ρ are all scalars — they have magnitude and sign (positive or negative) but no direction. Direction only appears later when you compute the electric field, which is a vector. Do not attach a direction to λ, σ or ρ themselves.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Linear charge density λ is in coulomb per metre (C/m). Surface charge density σ is in coulomb per square metre (C/m²). Volume charge density ρ is in coulomb per cubic metre (C/m³).
Yes. If the distributed charge is negative, the density is negative. λ, σ and ρ carry the sign of the charge because Q itself can be positive or negative.
It means the density has the same value at every point of the object. Then total charge is simply density times total length, area, or volume, and no integration is needed.
Gauss's law problems (infinite line charge, charged sheet, solid or hollow sphere) all start from the correct density λ, σ or ρ. Choosing the wrong density gives the wrong field, so this concept is the base for the next topic, Gauss's law.
