Question

Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 180 A and a height of 80 m above the ground, what magnetic field does the line produce at ground level?

Answer 1

B = 4.5 x 10⁻⁷ T = 0.45 μT

Step-by-step explanation:

From Ampere's law the magnetic field at a certain radius from straight current-carrying wire is given by the following formula:

`B = (\mu_oI)/(2\pi r)`

where,

B = magnetic field = ?

`\mu_o` = permeability of free space = 4π x 10⁻⁷ H/m

I = current = 180 A

r = radius = 80 m

Therefore,

`B=((4\pi\ x\ 10^(-7)\ H/m)(180\ A))/(2\pi (80\ m))\\\\`

B = 4.5 x 10⁻⁷ T = 0.45 μT