Current Density

Have you ever wondered what current density is and how you can determine it? Before you can understand the current density formula, you must possess proper knowledge of current itself.

Defining Current

Current is the flow of electrons from an electrically abundant source to an electrically deficit destination. We use the symbol I to denote current, whereas ampere is the standard unit for measuring the same. 

Current always follows in a specific direction of flow. Thus, you will find current flowing from a positive to a negative point. 

What are AC and DC current?

Before proceeding to learn what is current density, you should also be able to point out the differences between the two types of current – direct (DC) and alternating (AC). 

DC

AC

Direct current travels in the same direction, regardless of the point where you check the flow.

Alternating charge carriers often flow in the opposite direction to its established flow.

Here the flow maintains a constant magnitude.

Here, the flow’s magnitude differs with time.

Frequency of DC will always be zero.

Frequency of AC can vary, but it is always above zero.

  

Current Density Definition

Current density is referred to as the total amount of current which is flowing through one unit value of a cross-sectional area. If this is of uniform current flow, then the amount of current which is flowing through a specific conductor is the same at all points of the conductor, even if the conductor area differs.

Current density formula can help to determine the amount of current in a specific portion of the conductor. 

What is the Current Density Formula?

Current Density (J) = I/A

In this equation, ‘I’ is the amount of current in Amperes while ‘A’ is the cross-section area in sq. metres.  

Current Density Example

Now that you are aware of the formula for calculation, take a look at the example below to get a clearer idea. 

Example – A 10mm2 of copper wire conducts a current flow of 2mA. Determine this current density using the current density formula.

Solution – In this example, current (I) = 2 x 10-3 

A = 10 x 10-3

Thus, current density (J) = 2 x 10-3/10 x 10-3

J = 0.20 A/m2

What is the Unit of Current Density?

The SI unit of current density is Ampere/metre2. This unit also helps you remember the formula for calculation of such a density. Since Ampere is the unit of current and metre2 is the unit for measuring cross-sectional area, one can easily derive that the formula for current density. It is the current flow divided by the area of the cross section.

Quick Exercise – 1

What is this density when 137 Ampere of current flows through a conductor cross-section, measuring 1.2m2?

Solution – 

Here I = 137A

A = 1.2m2

Therefore, J = I/A

=> J = 137/1.2

=> J = 114.66 A/m2

What is the Relation between Current Density and Electric Field?

With the help of Ohm’s Law, you can determine a connection between electric field and current density.

We know I = nAevd

I = nAe(eE/m)

We know J = I/A

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

This is why charge density is so crucial in physics. It relates to the electric field in electromagnetism. 

True or False

Q. Unit of measuring frequency for alternating current is Joule.

Ans. False. The unit for measuring the frequencies of AC is Hertz and not Joule. 

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FAQ (Frequently Asked Questions)

1. How can you define current density?

Current density refers to the amount of charge flowing through a specific cross-sectional area of a conductor. The amount tends to remain constant in case of a steady charge flow. Nevertheless, this cross-sectional area of a conductor differs, which, in turn, leads to varying density.

2. Is current density scalar or vector quantity?

Current density is a vector quantity even though it is a combination of two scalar quantities.  

3. What is the symbol for current density?

This density is represented by ‘J’. Its unit, on the other hand is Ampere/metre2 or A/m2.