How to Calculate Current Density?

Current Density is calculated using formula J = I/A , where J is current density, I is current in amperes flowing and A is area in meter square. The SI unit of Current Density is amperes per square meter (A/m²). Current Density is current flowing per square unit of area. In this article we are going to discuss what is Electricity , what is current density and some sample problems on this concept.

What is Electricity?

Electricity is referred to as a form of energy that results due to the flow of electrons. There are two kinds of electricity, namely, static electricity and current electricity. Current is defined as the rate of charge flow from negative points to positive points in an electric circuit. It is measured in terms of amperes (A) and is denoted by the letter (I). There are two kinds of current, namely, alternating current and direct current. 

How to Calculate Current Density

In physics, current density, or the electric current density, is related to electromagnetism and defined as the measure of current flowing through a unit value of the area of the cross-section. Current density has both magnitude and direction since it is a vector quantity. In the case of a steady current, the flow of current is uniform throughout the conductor even if the area of cross-section differs. With the help of the current density, we can calculate the amount of current flowing in a specified portion of the conductor. It is represented by the letter “J” and its SI unit is A/m².

Let us consider a conducting wire and connect both ends of the wire to a battery. Now an electric field will be produced, which results in the flow of electrons through the conductor. Now, if σ is the electrical conductivity of the conducting wire, then the current density is directionally proportional to the electric field.

Current density (J) = σ E

Where σ is the electrical conductivity,

E is the electric field. 

The formula for current density is given as,

Current density (J) = I/A 

Where “I” is the current flowing the conductor,

“A” is the cross-sectional area of the conductor.

The dimensional formula of the current density is M⁰L^-2T⁰I¹,  where M is mass, L is length, T is time, and I is current.

Solved Problems on Current Density

Problem 1: Calculate the current density if a current of 60 A is flowing through a copper wire with a cross-sectional area of 20 m².

Solution:

Given data,

Current flowing through the wire (I) = 60 A 

The cross-sectional area of the wire (A) = 20 m²

We know that,

Current density (J) = I/A

J = (60)/(20)

J = 3 A/m²

Hence, the current density is 3 A/m².

Problem 2: Determine the current density if a current of 5A is flowing through a copper wire whose diameter is 3 mm.

Solution:

Given data,

Current flowing through the wire (I) = 5A 

Diameter of the wire = 3mm

⇒ Radius = 3/2 = 1.5 mm = 0.0015 m

Area of the cross-section of the wire = πr²

A = 3.14 × (0.0015)²

A = 0.000007065 m²

We know that,

Current density (J) = I/A

J = 5/0.000007065

J = 7.07 × 10⁵ A/m²

Thus, the current density is 7.07 × 10⁵ A/m².

Problem 3: Find the current flowing through the metal wire if its cross-sectional area is 15 m² and the current density is 5 A/m².

Solution:

Given data,

Cross-sectional area (A) = 15 m²

Current density (J) = 5 A/m²

We know that,

Current density (J) = I/A

5 = I/15

I= 5 × 15 = 75 A

Hence, the current flowing through the wire is 75 A.

Problem 4: Find the cross-sectional area of the wire if the current flowing through the wire is 4 mA and its current density is 0.25 A/m².

Solution:

Given data,

Current flowing the wire (I) = 4 mA = 0.004 A

Current density (J) = 0.25 A/m²

We know that,

Current density (J) = I/A

0.25 = 0.004/A

A = 0.004/0.25

A = 0.016 m² = 16 mm²

Hence, the cross-sectional area of the wire is 16 mm².

Problem 5: Determine the current density if a current of 85 A is flowing through a conductor with a cross-sectional area of 17 m².

Solution:

Given data,

Current flowing through the wire (I) = 85 A

The cross-sectional area of the wire (A) = 17 m2

We know that,

Current density (J) = I/A

J = 85/17

J = 5 A/m²

Therefore, the current density is 5 A/m².

Problem 6: What is the definition of current density and its SI unit of measurement?

Solution:

In physics, current density, or the electric current density, is defined as the measure of current flowing through a unit value of the area of the cross-section. It is represented by the letter “J” and its S.I unit is ampere per square meters (A/m²).