Question

A 0.40 mm diameter copper wire carries a current of 3μA. Find the current density in the wire.

a. 15.16A/m^2
b. 33.32A/m^2
c. 26.17A/m^2
d. 23.87A/m^2

Answer 1

Answer on Question 32811, Physics, Electric Circuits

Question:

A 0.40 mm diameter copper wire carries a current of 3 µA. Find the current density in the wire:

a) 15.16 A/m².

b) 33.32 A/m².

c) 26.17 A/m².

d) 23.87 A/m².

Solution:

By the definition of the current density we have:

$$J = \frac{I}{A},$$

here, $J$ is the current density, $I$ is the current flowing through the wire, $A = \pi \frac{d^2}{4}$ is the cross-sectional area of the wire, $d$ is the diameter of the wire.

Then, we can substitute $A$ into the first formula and find the current density in the wire:

$$J = \frac{I}{A} = \frac{4I}{\pi d^2} = \frac{4 \cdot 3 \cdot 10^{-6} \, A}{\pi \cdot (4 \cdot 10^{-4} \, m)^2} = 23.87 \, \frac{A}{m^2}.$$

Answer:

d) 23.87 A/m².

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