Question

Define the term surface charge density.

Answer 1

Hint: In this question, we will talk about the continuous charge distribution of charge. Depending upon the distribution of charge in one, two or three dimensions, we will see their classification and also the expression for the surface density which is mostly used in electrostatics.

 Complete step-by-step solution -
In many of the applications, electric forces are exerted by a charged body in the form of rods, plates, or solids. For simplicity we assume the body to be insulator and that the charge is spread throughout the surface or volume of the object, forming a continuous charge distribution.
Depending on whether we are considering charges that are respectively distributed in one, two, or three dimensions the charge density is of three types:
1. Linear charge density:
In this case, the charges are distributed in one dimension, such as the thin charged rods. If a charge ‘q’ is uniformly distributed on the rod of length L, then we can write:
$\lambda = \dfrac{q}{L}$ . Where ,
$\lambda $ is the linear charge density.
2. surface charge density
Here charge is distributed over two dimensional areas, such as the surface of the sheet.
It is defined as the charge per unit area. If a charge q is spread uniformly over a surface of area A then, we can say:
$\sigma = \dfrac{q}{A}$
Where $\sigma $ is the surface charge density, The SI unit of surface charge density is $C/{m^2}$ .
3. Volume charge density
Here the charge is distributed throughout the volume of the object. If the charge q is distributed uniformly throughout the volume V then,
$\rho = \dfrac{q}{V}$
Where,
$\rho $ is the volume charge density.

Note: The SI unit for volume charge density is $C/{m^3}$ and for linear charge density is C/m. To calculate the electric field due to a surface charge, for example a disk, here we divide the disk into a series of concentric rings and then calculate the electric field due this ring and then integrate it from 0 to R to get the total electric field.