# Current Density

## Introduction

When a constant value of current passes through a conductor, the same ampere of current will flow in the conductor. The flow of current is the same, but the sections may differ in some parts. The flow of current is a macroscopic feature.

## Current

The rate at which the electrons flow in a particular circuit or the flow of electrically charged particles is called current. It is represented by the symbol I. And Ampere is a standard unit used to measure current. The current will always flow in one particular direction.

## Types of Current

Current can be classified into two types:

### Alternating Current(AC)

The alternating current will always flow in the opposite direction.

The current flow varies with time, with magnitude.

The frequency will vary and, it is always above zero.

### Direct Current(DC)

The direct current will always flow in the same direction.

For direct current, the flow of the magnitude is always constant.

The frequency will always be zero.

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## Current Density

The flow of current or charge flow across the particular section of a conductor can be stated as Current density. The flow of electrons is generally stated as electric current.

When the ends of a battery are connected using a conductor, the electron passes from one side of the battery, into the other end of the battery through the wire. If the magnitude and direction of flow of electrons are constant, the value of current is also constant.

## Symbol and Unit of Current Density

The measurement of Current Density plays an important role in the concept of electromagnetism. Current Density is the amount of the flow of electric charge per unit area of amperes (A) in a particular field of cross-section, i.e. ${m^2}$.

J is the symbol used to represent the Current Density

Current density has magnitude and direction, so it is a vector quantity. The unit of current density is ampere / meter square (A/m2). The passing of electric current has units of charge per unit time (t) per unit area (A). It is measured perpendicular to the direction of the flow of current.

## Formula for Current Density

When the material of the conductor has an electrical conductivity given by the constant σ, then the density of electric current can be related to the electric field by:

$\mathrm{{J=\Sigma \times E}}$

Where

J is current density,

Sigma ${(\Sigma)}$ is conductivity,

E is an Electric field

Similarly, the other way of expressing the current density formula is:

J = I/A

Where

J is the current density in A/m2,

A is the cross-sectional area in m2

I denote the flow of electric current through the conductor in Amperes (A)

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## Current Density Calculator

Current density is the measurement of the density of an electric current in a particular unit. And this is also stated as the amount of current flowing through a cross-section of a conductor.

The formula to calculate Current density is, J = I/A

Finding the answer in terms of typical units (amp and m2) is easy to find in the current density calculator.

### Example of Current Density

Now you know the formula for calculating current density, take a look at the example to get a clearer understanding of calculating current density.

A 20mm2 of copper wire conducting a current 2mA, determine this current density.

Current (I) = 2 x 10-3

Area A = 20 x 10-3

J = I/A

Current density (J) = 2 x 10-3 / 20 x 10-3

J = 0.10 A/m2

### Things to Remember

• Current is defined as the flow of charged particles.

• Current has two types: AC and DC

• The flow of charge in a conductor through any cross-section is called the current density of a conductor.

• The unit of current density is $\mathrm{A/m^2}$. The formula of current density is J = I/A

## FAQs

Q1. What is current?

Ans. Current is the flow of electrically charged particles, from the low number of electrons to a high number of electrons in an atom. Electric current is represented by the term I.

Q2. What is the connection between Current Density and Electric Field?

Ans. The connection between electric field and current density is connected by ohm’s law.

We know I = nEavd

I = nAe(eE/m)

Current Density J = I/A

Now, I/A = ne2 (E/m)

This is why Current density is important in electromagnetism. Current density relates to the electric field in physics.

Q3. How can you define current density?

Ans. Current density is the amount of charge flowing through a specific cross-sectional area of a conductor. The amount of charge remains constant if the flow of charge is steady. When the cross-sectional area of a conductor varies, current density also varies.

Q4. How is the current density (J) related to conductivity? Explain in detail.

Ans. In the concept of electromagnetism, the current density plays an important role in calculating current. Current density refers to the amount of the charge flow in amperes per unit area of cross-section, i.e. $\mathrm{A/m^2}$.

For example,

When the conductive material has a conductivity given by σ, then the density of electric current related to the electric field is given by $\mathrm{{J=\Sigma \times E}}$.

This is how current density is related to conductivity.

Q5. What is the dimensional formula for current density?

Ans. The current density dimensional formula is given by,

M0L-2T0I1

Where

M, L, T and I are the Mass, length, Time, and Current, respectively.

Updated on: 13-Oct-2022

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