Continuous Charge Distribution 

A continuous charge distribution refers to a system where charge is spread over a region, such as a line, surface, or volume. The electric field due to a continuous charge distribution can be calculated using integration.

Types of Continuous Charge Distributions:

1. Linear Charge Distribution: Charge is distributed along a line.

2. Surface Charge Distribution: Charge is distributed over a surface.

3. Volume Charge Distribution: Charge is distributed throughout a volume.

Formula:

The electric field due to a continuous charge distribution is calculated using the formula:

E = ∫ dE

Where: 

dE = Electric field due to a small element of charge

 Applications: 

1. Calculating electric fields: For complex charge distributions.

2. Understanding charge behavior: In various systems, such as capacitors and conductors.

Some examples of continuous charge distributions:

1. Uniformly Charged Rod: Calculate the electric field at a point on the axis of a rod with uniform linear charge density.

2. Charged Disk: Find the electric field at a point on the axis of a disk with uniform surface charge density.

3. Spherical Shell: Calculate the electric field inside and outside a spherical shell with uniform surface charge density.