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
