Question

18. The electric field in a $2.0\mathrm{mm}\times 2.0\mathrm{mm}$square aluminum wire is $0.012\mathrm{V}/\mathrm{m}$. What is the current in the wire?

Short answer

The current in the wire is $1.68A$.

Step-by-step solution

Given information

The electric field in a $2.0\mathrm{mm}\times 2.0\mathrm{mm}$square aluminum wire is $0.012\mathrm{V}/\mathrm{m}$.

Explanation

The current density is given as a function of the current and cross-section area as: $J=\frac{I}{A}$ .
So, the current as $I=JA=J{a}^2$,
since in our case the cross-section will be a square.
The current density is related to the conductivity and electric field as
$J=\sigma E$
Substituting, to find for the intensity
$I=\sigma E{a}^2$
$I=3.5\times {10}^7\times 0.012\times 0.{002}^2$

$=1.68\mathrm{A}$.

Final answer

The current in the wire is $1.68A$.