Electric Field For Continuous Charge Distribution

How to Find the Electric Field Using Gauss Law?

Applications of Gauss Law to Find Electric Field

Let us talk about the different types of charge distribution

Linear Charge Distribution
Surface Charge Distribution
Volume Charge Distribution

Linear Charge Distribution

Linear charge distribution: If charge is distributed linearly over a body.

λ = dq/dl

λ = linear charge density
dq = charge
dl = line element

Consider an infinitesimally small element of charge (dq) along the line, the electric field contribution (dE) from this element can be calculated using Coulomb’s law: dE = k⋅dq/r² where k is Coulomb’s constant.

Integrate dE over the entire length of the line charge to obtain the total electric field E = ∫k⋅dq/r²

Surface Charge Distribution

Surface charge distribution: If charge is distributed continuously over the surface of a body

σ = dq/ds

σ = surface charge density
dq = charge
ds = surface element

Consider an infinitesimally small element of charge (dq) on the surface, the electric field contribution (dE) from this element can be calculated using Coulomb’s law: dE = k⋅dq/r², where k is Coulomb’s constant.

Integrate dE over the entire surface to obtain the total electric field E = ∫k⋅dq/r²

Volume Charge Distribution

Volume charge distribution: If charge is distributed continuously over the volume of a body.

ρ = dq/dv

ρ = volume charge density
dq = charge
dv = volume element

Consider an infinitesimally small volume element containing charge (dV) within the region, the electric field contribution (dE) from this volume element can be calculated using Coulomb’s law: dE = k⋅dq/r², where dq = ρ⋅dV and k is Coulomb’s constant.

Integrate dE over the entire volume to obtain the total electric field E = ∫k⋅dq/r²

Electric Field

Electric field is a fundamental concept in physics, defining the influence that electric charges exert on their surroundings. This field has both direction and magnitude. It guides the movement of charged entities, impacting everything from the spark of static electricity to the functionality of electronic devices Understanding electric fields will help you to understand how charge particles interact with each other and the surroundings and guide various natural and technological phenomena. In this article, we will learn in detail about electric field, its formula, calculation of electric field for ring, straight wire and continuous charge distribution.

Table of Content

What is an Electric Field?

Electric Field Formula