Answer:
The diameter of wire should be [tex]4.04 \times 10^{-4}[/tex] m
Explanation:
Given:
Current density [tex]J = 500 \times 10^{4}[/tex] [tex]\frac{A}{m^{2} }[/tex]
Current [tex]I = 0.64[/tex] A
From the formula of current density,
[tex]J = \frac{I}{A}[/tex]
Where [tex]A =[/tex] area of cylindrical wire = [tex]\pi r^{2}[/tex]
[tex]\pi r^{2} = \frac{I}{J}[/tex]
[tex]r^{2} = \frac{I}{\pi J }[/tex]
[tex]r = \sqrt{\frac{0.64}{3.14 \times 500 \times 10^{4} } }[/tex]
[tex]r = 2.02 \times 10^{-4}[/tex]m
For finding the diameter of wire,
[tex]d = 2r[/tex]
[tex]d = 4.04 \times 10^{-4}[/tex]m
Therefore, the diameter of wire should be [tex]4.04 \times 10^{-4}[/tex] m
