Current Density: Important Questions

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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 – 

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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