Question

Many industries are powered via distant power stations. Calculate the current flowing through a 7,300m long 10. copper power line that produces a 0.10T magnetic field. Note: No = 4 TX10-7T-m/A and copper = 1.72 x 10-82.m. Note: Do not assume the voltage transmitted on the power line. Note: This is a two-step problem: This is a two-step problem: Calculate the radius of the power line from the physical dimensions and then calculate the current from the magnetic field. A. 125A OB. 250A C.500A OD. 750A E. 1,000A

Answer 1

Current, I = 1000 A

Step-by-step 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

`\mu_o=4\pi * 10^(-7)\ T-m/A`

Resistivity,
`\rho=1.72* 10^(-8)\ \Omega-m`

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 :

`R=\rho (l)/(A)`

`R=\rho (l)/(\pi r^2)`

`r=\sqrt{(\rho l)/(R\pi)}`

`r=\sqrt{(1.72* 10^(-8)* 7300)/(10\pi)}`

r = 0.00199 m

or

`r=1.99* 10^(-3)\ m=2* 10^(-3)\ m`

The magnetic field on a current carrying wire is given by :

`B=(\mu_o I)/(2\pi r)`

`I=(2\pi rB)/(\mu_o)`

`I=(2\pi * 0.1* 2* 10^(-3))/(4\pi * 10^(-7))`

I = 1000 A

So, the current of 1000 A is flowing through the copper wire. Hence, this is the required solution.