What is continuous charge distribution?

As we all know that the charge is always quantized. Pertaining to the smallest amount of charge is that it can exist as +e or –e. It is the charge present on an electron and proton.
The total space covered by any charge in dimensions is very small as compared to the distance between the two charges from an observation point. That observation point can be taken as a point charge.

In a continuous charge distribution, all the charges are closely bound together i.e. having very less space between them. But this closely bound system doesn’t means that the electric charge is uninterrupted. It clears that the distribution of separate charges is continuous, having a minor space between them.

Types of continuous charged distributions:
1. Linear Charge Distribution
2. Surface Charge Distribution
3. Volume Distribution of charge

Linear Charge Distribution:
When the distribution of charge is uniformly along the line then it is called Linear Charge Distribution. E.g. line making the circumference of a circle, straight line, etc.
It is denoted by symbol .
= dq / dl. It is measured in Cm^-1 .Lets take a small element having length dl of the line L. The small amount of charge on this element is

dq= . dl.

So the resultant force can be calculated by using the formula:

Total force on small charge elements by adding them vectorially is:

Surface Charge Distribution:
When the charge distribution is over a particular area then the distribution is called as Surface charge distribution.

It is denoted by .

= dq / ds. It is measured in Cm ^-2 . Total force F on a small test charge q₀ is due to surface distribution of charge. It is shown below:


Volume Distribution of charge:
When charge is distributed over a certain volume i.e. over a sphere, over a cube etc, then it is called Volume distribution of charge.
Symbol to represent it is
Charge per unit volume is:
= dq / dV.

Note: In all the three cases unit vector is a variable unit, directed from each point on a line, surface or volume against the test charge q₀. The values of different distributions,,
, may vary at different points.

The simple expression for the resultant force applied on a test charge

by n number of different point charges and the three kinds of charge distributions is the vector sum of all the distinct forces.

Things to Remember
• Charge resides on the outer surface of conductor. So, complete charge of a body can be transferred to another body if they are enclosed with each other.