Question

Although the evidence is weak, there has been a concern in recent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is 20 m above the ground and carries a 200 A current at a potential of 110 kV.
a. What is the magnetic field strength on the ground directly under such a transmission line?
b. What percentage is this of the earth's magnetic field of 50 ?T?

Answer 1

Answer:

a

The magnetic field strength is  $B = 2 \mu T$

Explanation:

From the question we are told that

             The  length line   above the ground  is  $R = 20m$

              The current of the line is  $I = 200A$

              The voltage of the line is $V = 110kV$

Generally magnetic field strength is mathematically represented as

              $B = \frac{\mu_o I}{2 \pi R}$

Where  $\mu_0$ is the permeability of free space  $= 4\pi * 10^{-7} N/A^2$

             $B = \frac{(4\pi * 10^{-7} N/A^2) *200}{2 \pi *20}$

                $= (2.0*10^{-7})[\frac{200}{20} ]$

               $= 2*10^{-6}T$

              $= 2 \mu T$

Earths magnetic field is approximately given as $50 \mu T$

   So the percentage would be

                           $= \frac{Magnetic \ Field \ Intensity \ Of \ Line}{Earth's \ Magnetic \ Field} * 100$

                          $= \frac{2 \mu T }{50 \mu T } * 100$

                          $=4$%