CBSE Class 12-science Answered

A system of a large number of closely spaced charges is known as continuous charge distribution.

A continuous charge distribution may be of the following three types:

1.   Linear charge distribution- is a charge distribution in which charge is distributed uniformly along a line that is a charged wire or ring etc.

The linear charge density λ of a wire is given as

where Δl is a small line element of a wire on macroscopic scale                                        

and ΔQ is the charge contained in the line element. The unit for λ is C/m.                                      

If q₀ is a point charge at point P situated at a distance r from Δl then force due to this element will be

2.    Surface charge distribution- is defined as continuous charge distribution over some area. For example a charged thin sheet.

The surface charge density σ of a wire is given as

where Δs is a small area element of a charged sheet on macroscopic scale and ΔQ is the charge contained in that area element. The unit for σ is C/m2.

If q₀ is a point charge at point P situated at a distance r from Δs then force due to this element will be

3.  Volume charge distribution- is defined as continuous charge distribution over a volume. For example a metal sphere or cylinder etc.

The volume charge density or simply called charge density ρ is given as

 where ΔV is a small volume element of a charged sphere on macroscopic scale and ΔQ is the charge contained in that volume element. The unit for ρ is C/m3. 

If q₀ is a point charge at point P situated at a distance r from ΔV then force due to this element will be 

                          .