Answer:
Current, I = 1000 A
Explanation:
It is given that,
Length of the copper wire, l = 7300 m
Resistance of copper line, R = 10 ohms
Magnetic field, B = 0.1 T
[tex]\mu_o=4\pi \times 10^{-7}\ T-m/A[/tex]
Resistivity, [tex]\rho=1.72\times 10^{-8}\ \Omega-m[/tex]
We need to find the current flowing the copper wire. Firstly, we need to find the radius of he power line using physical dimensions as :
[tex]R=\rho \dfrac{l}{A}[/tex]
[tex]R=\rho \dfrac{l}{\pi r^2}[/tex]
[tex]r=\sqrt{\dfrac{\rho l}{R\pi}}[/tex]
[tex]r=\sqrt{\dfrac{1.72\times 10^{-8}\times 7300}{10\pi}}[/tex]
r = 0.00199 m
or
[tex]r=1.99\times 10^{-3}\ m=2\times 10^{-3}\ m[/tex]
The magnetic field on a current carrying wire is given by :
[tex]B=\dfrac{\mu_o I}{2\pi r}[/tex]
[tex]I=\dfrac{2\pi rB}{\mu_o}[/tex]
[tex]I=\dfrac{2\pi \times 0.1\times 2\times 10^{-3}}{4\pi \times 10^{-7}}[/tex]
I = 1000 A
So, the current of 1000 A is flowing through the copper wire. Hence, this is the required solution.
