As we have already dealt with systems having discrete charges q1, q2, …, qn whose mathematical treatment is very simple and does not need calculus. But, for many purposes, it is impractical to work with discrete charges and we need to work with continuous charge distributions. For example – It is impractical to specify the charge distributions on the surface of the conductor in terms of microscopic charged constituents. So, it is more practical to consider an area element ∆S and charge ∆Q on that element. Thus, the continuous charge distribution is defined as the system in which the charge is uniformly distributed over the conductor.
Linear charge density
When the charge is uniformly distributed over the length of the conductor is known as linear charge density. It is also defined as the charge per unit length at any point on the linear charge distribution.
- It is denoted by λ ( Lambda ).
- Its SI unit is C/m.
- It is also known as linear charge distribution.
- Mathematically, linear charge density is given as
Surface charge density
When the charge is uniformly distributed over the surface of the conductor is known as surface charge density. It is also defined as the charge per unit area at any point on the surface charge distribution.
- It is denoted by σ ( Sigma ).
- Its SI unit is C/m2.
- It is also known as surface charge distribution.
- Mathematically, surface charge density is given as
Volume charge density
When the charge is uniformly distributed over the volume of the conductor is known as volume charge density. It is also defined as the charge per unit volume at any point on the volume charge distribution.
- It is denoted by ρ ( Rho ).
- Its SI unit is C/m3.
- It is also known as volume charge distribution or charge density.
- Mathematically, volume charge density is given as
Electric field
- Electric field due to charge ρΔV is
- Total electric field due to charge distribution of all volume elements is
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