Question

A small but measurable current of 1.2 10-10A exists in a copper wire whose diameter is 2.0 mm. Assume the current is uniform. (a) Calculate the current density.

Answer 1

Q: A small but measurable current of 1.2×10⁻¹⁰A exists in a copper wire whose diameter is 2.0 mm. Assume the current is uniform. (a) Calculate the current density.

Answer:

3.82×10⁻⁵ A/m

Explanation:

Current density: This can be defined as the amount of charge passing through a conductor, per unit area, per unit time. The S.I unit of current density is A/m²

From the question above, the expression for current density is given as,

τ = I/A............... Equation 1

Where τ = current density of the copper wire, I = current flowing  through the copper wire, A = cross sectional area of the copper wire

But,

A = πd²/4................. Equation 2

Substitute equation 2 into equation 1

τ = 4I/(πd²)............ Equation 3

Given: I = 1.2×10⁻¹⁰ A, d = 2 mm = 2×10⁻³ m, π = 3.14

Substitute into equation 3

τ = 4(1.2×10⁻¹⁰)/[3.14×(2×10⁻³)²]

τ = (4.8×10⁻¹⁰)/(1.256×10⁻⁵)

τ = 3.82×10⁻⁵ A/m

Answer 2

Explanation:

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