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15.1 | Electric Current. Current Density |

In these revision notes for Electric Current. Current Density, we cover the following key points:

- Definition of electric current
- Why electric current is that important in daily life?
- What is charge density? How many types of charge density are there?
- What is the difference between charge density and current density?
- What is direct current?
- What direction does the current flow in a circuit?
- How can we find the electric field using the help of charge density and Gauss Law?

Stationary charges do not do any work. Most applications related to electricity in today's world use moving charges (dynamic electricity or electrodynamics) to operate. With moving charges, we usually have in mind electrons, as they are able to move freely between the atoms of conductor. Hence, electrons are widely recognized as the main carriers of electricity. (In some specific cases, positive ions are electricity carriers as well).

Electric charges (typically electrons) always flow from places where there are more electrons to the places in which there are less electrons. If there is some misbalance (a potential difference) between the numbers of free charges in the two extremities of a conductor, a charge flow takes place until both extremities have the same density of free charges.

By definition, **electric current, is the amount of electric charges flowing through any point of conductor in the unit time**.

The symbol of electric current in formulae is I. This is because the term "electric current" is an abbreviation of the longer term "**intensity of electric current**", but we use the short term "**electric current**" or simply "**current**" in conversational form.

Mathematically, we have

I = *Q**/**t*

The unit of electric current, **Ampere (amp)**, A, is one of the seven fundamental units in the SI system used in science.

It is easy to see that Coulomb = Ampere ∙ second in the SI system of units.

It is not the number of free charges in both ends of a conductor the main factor that determines the electricity flow but it is the current density instead. **Current density** (J) is a dynamic quantity and it must not be confused with the term of charge density, which on the other hand is a static quantity. Charge density shows how close electric charges are to each other in a conductor. There are three variants of charge density.

**i. Linear charge density, λ**. It shows how close the charges are to each other in a long and very thin conducting wire of length L. Linear charge density is calculated by the equation

λ = *Q**/**L*

and it is measured by Coulombs per metre [C/m].

**ii. Surface charge density, σ**. It shows how close the charges are to each other in a surface of area A. Surface charge density is calculated by the equation

σ = *Q**/**A*

and it is measured by **Coulombs per square metre** [C/m2].

**iii. Volume charge density, ρ**. It shows how close the charges are to each other in a space of volume V. Volume charge density is calculated by the equation

ρ = *Q**/**V*

and it is measured by **Coulombs per cubic metre** [C/m3].

It is more realistic to discuss about area charge density than for the other two types of charge density, as it is a known fact that electric charges are distributed throughout the outer surface of a conductor.

**Current density** (J) is a vector quantity that gives the rate of current flow through a certain area A. Mathematically, the current density is calculated by

J = *I**/**A*

where I is the current and A is the area in which the current flows (usually the cross-sectional area of conductor). However, in vector form we use another equation to describe the current density. It is

J*⃗* = ρ ∙ v*⃗*

where ρ is the volume charge density and v is known as the "**drift velocity**", i.e. the net velocity of charges movement in a certain direction (usually in the direction determined by the push of the electric source along the conducting wire).

Current density is measured in **Amps per square metre** [A/m2].

Direct current (DC) is the simplest type of current. The main producers of direct current are batteries, whose positive and negative terminals are well defined. This means the current has a single direction of flow throughout an electrical circuit.

The positive-to-negative direction is called the "**conventional direction of current flow**" and it is opposite to the direction of **electrons flow** (which is from negative to positive terminal of battery).

Electric field can be expressed in terms of charge density with the help of Gauss Law. Thus, the electric field produced by a long bar of linear charge density λ at a distance r from it, is

E = *λ**/**2π ∙ r ∙ ϵ*_{0}

On the other hand, the electric field produced by a charged surface of charge density σ, is

E = *σ**/**ϵ*_{0}

The above formula means that **the magnitude of electric field outside a conductor is proportional to the surface charge density on the conductor**. This is one of the most important assertions in Electromagnetism.

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