A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? ( μ 0 = 4π × 10 -7 T ∙ m/A)

Respuesta :

Answer:

The strength of the magnetic field that the line produces is [tex]2x10^{-5} Tesla[/tex].

Explanation:

From Biot-Savart law, the equation to determine the strength of the magnetic field for any straight wire can be deduced:

           

[tex]B = \frac{\mu_{0}I}{2\pi r}[/tex] (1)      

                                     

Where [tex]\mu_{0}[/tex] is the permiability constant, I is the current and r is the distance from the wire.    

             

Notice that it is necessary to express the current, I, from kiloampere to ampere.

[tex]I = 1.0kA \cdot \frac{1000A}{1kA}[/tex] ⇒ [tex]1000A[/tex]

Finally, equation 1 can be used:

[tex]B = \frac{(4\pi x10^{-7}T.m/A)(1000A)}{2\pi (10m)}[/tex]    

           

[tex]B = 2x10^{-5}T[/tex]    

Hence, the strength of the magnetic field that the line produces is [tex]2x10^{-5} Tesla[/tex].