Current Density: Important Questions

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Current Density Important Questions and Answers are covered in this article along with a detailed explanation. Current density is the total current which is flowing through one unit of cross-sectional area. If the current flow is uniform, the amount of current that flows through a specific conductor is the same at all points of the conductor, even if the area of the conductor.
Current density formula in a specific portion of the conductor, Current Density (J) = I/A

Here, ‘I’ is the amount of current in Ampere
‘A’ is the cross-section area in sq. meters.

Very Short Answer Questions (1 Mark)

Ques. What is the symbol for current density?

Ans. Current Density is represented by the symbol ‘J’.

Ques. Is the current density scalar or a vector quantity?

Ans. Current density is a vector quantity even though it combines two scalar quantities.

Ques. Define current density.

Ans. Current density is the amount of charge that flows through a specific cross-sectional area of the conductor. In the case of a steady charge flow, the amount of charge remains constant. Nevertheless, the cross-sectional area differs, which, in turn, leads to different values of current density.

Ques. What is the Unit of Current Density?

Ans. Current Density is measured in Ampere/meter².

Ques. What is the formula for current density?

Ans. The current density formula is given as – J = I/A

Ques. Define current.

Ans. Current is the flow of electrons from an electrically rich source to an electrical deficit one.

Ques. Write the dimensional formula of Current density.

Ans. Current density, J = I/A

⇒ [J] = [A]/[L²] = [L^-2A] or [M⁰L^-2T⁰A]

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Short Answer Questions (2 Marks)

Ques. A 10mm² of copper wire conducts a 2 mA current flow. Determine the current density.

Ans. Current (I) = 2 x 10^-3

A = 10 x 10^-3

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

J = 0.20 A/m²

Ques. What is the relation between current density and electric field?

Ans. With Ohm’s Law, a connection between the electric field and current density can be determined.

I = neAv_d

But, v_d = eEτ/m

⇒ I = neA(eEτ/m) = ne²AEτ/m

⇒ I/A = ne²Eτ/m

We know that J = I/A

⇒ J = ne²Eτ/m

Also, conductivity, σ = ne²τ/m

⇒ J = σE

Ques. Find out the current density when 137 Ampere of current flows through a conductor of a 1.2m² cross-section area.

Ans. Given, I = 137A

A = 1.2m²

We know that, J = I/A

J = 137/1.2

J = 114.66 A/m²

Ques. Find the current density in a wire of diameter 0.2 cm in which a current of 10 A flows.

Ans. Given,

Diameter, d = 0.2 cm = 2 x 10³ m
Current , I = 10 A

Using J = I/A = 4I/πD² = (4 x 10)/(3.14 x 4 x 10^-6)

⇒ J = 3.18 x 10⁶ Am^-2

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Long Answer Questions (3 Marks)

Ques. Define and differentiate between AC and DC Current.

Ans. The differences between AC and DC current can be classified as follows –

AC Current	DC Current
AC charge carriers flow in the opposite direction.	DC charge carriers flow in the same direction.
The magnitude of the flow differs with time.	The magnitude of the flow differs with time.
The frequency of Alternating Current can vary, however, it is always above zero.	The frequency of Direct Current is always zero

Ques. What is the relation between the current density and electron mobility?

Ans. We know that I = neAv_d

and current density J = I/A

J = (neAv_d)/A

J = nev_d

J = ne(eEτ/m) [v_d= eEτ/m]

J = neE(eτ/m)

J = neEμ

Ques. Find out the relation between the current density and the relaxation time.

Ans. Given: I = neAv_d

and current density J = I/A

J = (neAv_d)/A

J = nev_d

J = ne(eEτ/m) [As v_d= eEτ/m]

J = ne²Eτ/m

Ques. Calculate the current density in a uniform wire connected to a battery of 3.5 V EMF and negligible internal resistance. The resistance of a wire is 2.0 Ω with a cross-sectional area of 0.70 x 10^-6 m².

Ans. Given: Electromotive Force – 3.5 V

Resistance – 2.0 Ω

Area of cross-section = 0.70 x 10^-6 m²

Current, I = V/R

I = 3.5/2

I = 1.75 A

Current Density, J = I/A

= 1.75/(0.70 x 10^-6 m²)

J = 2.5 x 10⁶ m²

Ques. Find out the current density when 100 Amperes current flows through the battery in a 10 m² area.

Ans. Given: Current I = 100 A,

Area, A = 10 m²

Now, through the current density formula, J = IA

J = 100/10

J = 10 A/m²

Therefore, the current density is 10 A/m².

Ques. A 15 mm² copper wire has 5 mA of current flowing through it. Find its current density.

Ans. Given parameters: Total Current, I = 5 mA

Total Area, A = 15 mm²

Current density formula, J = I/A

J = 5 × 10⁻³/15×10⁻³

J = 0.33 A/m²

Therefore, the current density is 0.33 A/m²

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