Question

EMF. Currents in dc transmission lines can be 100 A or more. Some people have expressed concern that the electromagnetic fields (EMFs) from such lines near their homes could cause health dangers.
Part A
For a line with current 180 A and at a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas.

B=____T

Part B
What magnetic field does the line produce at ground level as a percent of the earth's magnetic field, which is 0.50 gauss.

B/Be=____%

Answer 1

Answer:

The magnetic field B of the transmission line is 4.5·10^(-6)T. The ratio B/Be is 0.0009% (there is no risk to human health)

Explanation:

we will consider a dc transmission line as an infinite longitudinal line in the Z-axis with a dc current of 180 A. To solve the problem we will use ampere's law. We can consider the geometry of the problem (Rotational symmetry in respect of Z-axis) than the field B is annular with center in the transmission line.

$\vec{B}(r,\varphi,z)=B(r)\vec{\varphi}$

$\displaystyle\oint_{C} \vec{B}(r)\,\vec{dl}=\mu I_c$

We will use a circular amperian curve C. Therefore:

$\displaystyle\oint_{C} \vec{B}(r)\,\vec{dl}=\int_{0}^{2\pi} B(r)\vec{\varphi}\,\vec{\varphi}rd\varphi=B(r)r\int_{0}^{2\pi} \,d\varphi=B(r)r2\pi=\mu I_c$

$B(r)=\displaystyle\frac{\mu 180A}{r2\pi}$

For a height of 8.0m (r=8m):

$B(8m)=\displaystyle\frac{\mu 180A}{8m2\pi}=4.5\cdot10^{-6}T$

Compared to the earth magnetic field:

$\displaystyle\frac{B}{B_e}\%= \frac{B}{B_e}100=0.0009\%$