Q22E Currents in dc transmission line... [FREE SOLUTION]

91影视

University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 4: Q22E (page 949)

Currents in dc transmission lines can be 100 A or higher. Some people areconcerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150A and a height of 8 m above the ground, what magnetic field does the line produce at ground level? Express your answer in tesla and as a percentage of the earth鈥檚 magnetic field, which is 05 G . Is this value cause for worry?

Short Answer

Expert verified

The magnetic field of earth has a magnitude of about $B = 5 脳 10^{- 5} T$ , so the field produced by the transmission line is 7.5 % of the Earth鈥檚 magnetic field.

Step by step solution

The formula to be used in the problem

We need to find the magnetic field at the ground due to a transmission line that has current of $I = 150 A$ at a height of $r = 8 m$ above the ground. We will treat the line as a very long and straight wire.

The magnetic field due to a very long wire is given by $B = \frac{渭_{0} I}{2 蟺谤}$ .

Find the magnetic field using the formula

$\begin{aligned} B = \frac{渭_{0} I}{2 蟺 r} \\ B = \frac{2 脳 10^{鈭� 7} 脳 150}{8} \\ B = 3.8 脳 10^{鈭� 6} T \end{aligned}$

The magnetic field of earth has a magnitude of about $B = 5 脳 10^{- 5} T$ , so the field produced by the transmission line is 7.5 % of the Earth鈥檚 magnetic field.