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Current density is the amount of electric current that flows through a unit value of the cross-sectional area. It is a vector quantity comprising both a direction and scalar magnitude. Current Density is measured in terms of Ampere per square meter (A/m2). In the case of a steady current, the same current flows in all the parts of the conductor. This flow is the same although the cross-sections may vary in some parts of the area.
| Table of Content |
Key Takeaways: Current, Current Density, Ampere, Cross Section, Electromagnetism, Alternating Current, Direct Current, Electric Current, Conductor, Magnetic Field, Electrical Conductor, Electromagnetic field
What is Current Density?
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Current density in a conductor can be defined as the charge flow through any cross-section of the conductor. However, the current density alters in different parts of an electrical conductor resulting in alternating currents at higher frequencies. Electric current always creates a magnetic field. With a stronger current, the intensity of the magnetic field increases. Varying AC or DC leads to an electromagnetic field and this is the principle based on which signal propagation takes place.
Current Density
- Current Density is the flow of electric current per unit cross-section area.
- It is denoted in Amperes per square meter.
- The more the current is in a conductor, the higher the current density.
- The electric current generates a magnetic field. The stronger the current, the more intense will the magnetic field be.
- Current density is a vector quantity that has both a direction and a scalar magnitude.
- It is the amount of current flowing across the given region
Discover about the Chapter video:
Current Electricity Detailed Video Explanation:
Read more:
| Important Topics | ||
|---|---|---|
| Current Electricity | Electrical Current | Types of Current |
| Ohm’s Law | Unit of Current | Power of Alternating Current |
| AC vs DC | Relation between resistance and length | Power Transformers |
Current Density Symbol and Unit
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In the field of electromagnetism, the current density and its measurement play an important role.
- Current Density is the amount of the flow of electric charge in amperes per unit area(A) of cross-section i.e. m².
- Current Density is represented by the symbol J.
- Current density is a vector quantity because it has the magnitude and direction of the flow.
- An electric current that passes through has units of charge per unit time(t) per unit area(A).
- It is also measured in the direction that is perpendicular to the direction of flow.
- The unit of current density is ampere per square meter(A/m2).
Read More: Current Density MCQ
Current Density Formula
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Suppose that a medium (conductive material) has an electrical conductivity given by σ, then the density of electric current can be related to the electric field by the equation:
| J = Σ × E |
- where J is current density,
- Sigma (Σ) is conductivity,
- E is an Electric field
Similarly, the current density formula can be expressed in another way as follows:
| J = I/A |
where,
- J is the current density in A/m2,
- A is the cross-sectional area in m2
- I refer to the flowing electric current through the conductor in Amperes (A)
Current Density Solved ExamplesQues: Calculate the current density when 40 amperes of current is flowing through the battery in a given area of 10 m2. Solution: It is given that, I = 40 A, Area = 10 m2 The current density formula is given by, J = I / A = 40 / 10 J = 4 A/m2. Ques: A 10mm2 of copper wire conducts a current flow of 2mA. Calculate this current density using the current density formula. Solution: Here, 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 |
Read More: Current Density Important Questions
What is Current?
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The flow of electrically charged particles is referred to as current. Current is denoted by the symbol I and measured by its standard unit Ampere.
- Current always flows in a specific direction.
- The flow of the current is from an electrically abundant source to an electrically deficit one.
Current
Types of Current
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Current can be mainly divided into two types:
Alternating Current
The alternating current flows in the direction opposite to the established flow.
- The flow of the magnitude of the current varies with time.
- Though its frequency can change, it always remains above zero.
Direct Current
The direct current always flows in the same direction.
- The flow of the magnitude is always constant.
- The frequency of Direct Current will always remain zero.
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Things to Remember
- The flow of electrically charged particles is referred to as current.
- Current can be of two types: Alternating Current and Direct Current.
- Current density in a conductor can be defined as the charge flow through any cross-section of the conductor.
- The unit of current density or electric density is ampere per square meter(A/m2).
- The current density formula can be expressed as: J = \(\frac {I} {A}\)
- Current Density is represented by the symbol J.
Sample Questions
Ques. Is current density microscopic or macroscopic quantity? (1 mark)
Ans. Current density is a microscopic entity while current is a macroscopic quantity.
Ques. How electric current density is measured? (1 mark)
Ans: Electric current density is measured in ampere per square meter.
Ques. Find the current density passing through a copper wire having a cross-section area of 15 mm² and the current flowing through it is 5 mA. (2 mark)
Ans: Given: A = 4 square millimeters, I = 6 mA, J = ?
Thus, using the formula J= I/A
J = 0.005 / 0.015
J = 0.03 A/m2.
Thus, 0.03 A/m2 is the current density.
Ques. How is the current density(J) related to conductivity? Explain in detail. (3 mark)
Ans. In the field of electromagnetism, the current density and its measurement play an important role. It refers to the amount of the electric charge flow in amperes per unit area of cross-section i.e. A/m². For Example,
Suppose that a medium (conductive material) has an electrical conductivity given by σ, then the density of electric current can be related to the electric field by the equation: J = Σ × E.
Thus, the current density is related to conductivity.
Ques. What is the dimensional formula for current density? (2 mark)
Ans: The dimensional formula of current density is given by the formula,
[M0L-2T0I1]
where M is the Mass
- I is the Current
- L is the Length
- T is the Time
Ques. Why is current density important? (3 mark)
Ans: Current density finds its importance in the design of electrical and electronic systems.
Electronic Systems
Current density plays an important role in the design and production of electronic systems.
Electric circuit performance relies on the level of current and the purpose of its design. The dimensions of the capacitors control or manage the current density.
Ques. Why is copper known as a good conductor of heat? (2 mark)
Ans: Copper is a very good conductor of heat as well as current. Thus, a very small section of high current density may get hot, but it can also conduct that heat away to neighboring copper pours.
Ques. Why is current density a vector quantity? (2 mark)
Ans: Current Density describes how charges flow at a certain point since current density = \(\frac {I} {A}\). Thus, it has a magnitude and the vector direction tells you about the direction of flow at that point.
Ques. Determine the current density of 200 Amperes of current flowing through the battery in an area of 20 m2? (3 mark)
Ans: Given Current I = 200 A, Area, A = 20 m2
Now, applying the formula,
J = \(\frac {I} {A}\)
Substituting the given value in the formula, we get,
J = 200/ 20
= 20 A/m2
Thus current density is 20 A/m2.
Ques. Why is it best to use a current density conversion calculator? (2 mark)
Ans: When coping with current density, the units of your variables can vary from what is usually given in the current density equation. The best and simplest method to translate measurements is to make use of a good current density calculator.
Ques. What is the relation between Current Density and Electric Field? (2 marks)
Ans. With the help of Ohm’s Law, the relation between electric field and current density can be determined:
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.
Ques. Find the density when 137 Ampere of current flows through a conductor cross-section, measuring 1.2m2? (2 marks)
Ans. Here I = 137A
A = 1.2m2
Therefore, J = I/A
=> J = 137/1.2
=> J = 114.66 A/m2
Ques. A 5 mm2 copper wire has a current of 5 mA of current flowing through it. Determine the current density. (2 marks)
Ans. Given:
Total Current I is 5 mA
Total Area A is 5 mm2
The Current density J = I / A
= 5×10−3 / 5×10−3
= 1 A/m2
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