If the radius of a sphere is increased without changing the magnitude of charge on it, the surface charge density will:

CONCEPT:

Linear charge density:

• It is defined as the quantity of charge per unit length.
• Its SI unit is C/m.
• If ΔQ charge is contained in the line element Δl, the linear charge density λ will be,

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Surface charge density:

• It is defined as the quantity of charge per unit area.
• Its SI unit is C/m2.
• If ΔQ charge is contained in the elemental area Δs, the surface charge density σ will be,

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Volume charge density:

• It is defined as the quantity of charge per unit volume.
• Its SI unit is C/m3.
• If ΔQ charge is contained in the elemental volume Δv, the volume charge density ρ will be,

​\(\Rightarrow \rho=\frac{\Delta Q}{\Delta v}\)

EXPLANATION:

• Surface charge density is defined as the quantity of charge per unit area.

• If ΔQ charge is contained in the elemental area Δs, the surface charge density σ will be,

​

If ΔQ = constant

        ----(1)

• When the radius of a sphere is increased, its surface area will also increase.
• By equation 1 it is clear that the surface charge density is inversely proportional to the surface area when the charge on the body remains unchanged.
• So when the radius of a sphere is increased, its surface charge density will decrease. Hence, option 2 is correct.