Introduction of 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 current density is, you should also be able to point out the differences between the two types of current – direct (DC) and alternating (AC).
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. meters.
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/meter2. This unit also helps you remember the formula for calculation of such a density. Since Ampere is the unit of current and meter2 is the unit for measuring cross-sectional area, one can easily derive 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 = nEavd
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.
To form a better understanding of such concepts like density, Ohm’s law and more, join our online classes. Conducted by experts, each class looks to clear doubts for students. Now you can even download our Vedantu app for convenient access to these online classes and study material on every topic.
FAQs on Current Density
1. What is current density and how is it calculated for a conductor?
Current density is a vector quantity that measures the concentration of electric current. It is defined as the amount of electric current flowing per unit of cross-sectional area at a specific point within a conductor. For a uniform current 'I' flowing perpendicularly through a conductor's cross-sectional area 'A', the magnitude of current density (J) is calculated using the formula: J = I / A.
2. What is the key difference between electric current and current density?
The primary difference lies in their nature and scope.
- Electric Current (I) is a macroscopic property that describes the total rate of charge flow through the entire cross-section of a conductor. It is a scalar quantity.
- Current Density (J) is a microscopic property that describes the current flow at a specific point inside the conductor. It is a vector quantity, having both magnitude and direction.
3. What is the SI unit and the dimensional formula for current density?
The SI unit for current density is Ampere per square metre (A/m²). This is derived directly from its formula (Current/Area). The dimensional formula for current density is [M⁰ L⁻² T⁰ A¹], as it represents Ampere [A] divided by Length squared [L²].
4. Why is current density considered a vector quantity, while electric current is a scalar?
Electric current is a scalar because its direction is always constrained by the path of the conductor. We only need to specify its magnitude. However, current density is a vector because it describes the direction and magnitude of charge flow at a specific point inside the conductor. The direction of the current density vector (J) at any point is the direction in which a positive charge carrier would move at that point.
5. How are current density (J) and electric field (E) related within a conductor according to the CBSE 2025-26 syllabus?
The relationship between current density and the electric field is given by the vector form of Ohm's law. The formula is J = σE, where:
- J is the current density vector.
- E is the electric field vector.
- σ (sigma) is the conductivity of the material, which is a scalar constant.
6. In a conductor with a non-uniform cross-section carrying a steady current, does the current density remain constant? Explain why.
No, the current density does not remain constant. While the total electric current (I) remains the same throughout the conductor due to the principle of conservation of charge, the current density (J = I/A) changes. In the narrower sections of the conductor, the area (A) is smaller, resulting in a higher current density. Conversely, in the wider sections, the area is larger, leading to a lower current density.
7. Why is understanding current density important for practical applications like designing electrical circuits and wiring?
The concept of current density is crucial for safety and efficiency in electrical design. Every conducting wire has a maximum current density it can safely handle. Exceeding this limit causes excessive Joule heating (I²R loss), which can lead to the wire overheating, melting its insulation, or even causing a fire. Therefore, engineers use current density calculations to select the appropriate wire thickness for a given application, ensuring the system operates safely and reliably.
