Magnitude of the magnetic field produced by a wire

[Kiyah]

Homework Statement

A power line carries a current of 95 A along the tops of 8.5 m high poles. What is the magnitude of the magnetic field produced by this wire at the ground?


How does this compare with the Earth's field of about 1/2 G?

Homework Equations

B= uo$$\mu$$/2$$\pi$$I/r

The Attempt at a Solution

4$$\pi$$e-7/2$$\pi$$95/8.5

 

[Delphi51]

The formula is not appearing quite right on my screen, but you clearly have the right one. Is there any difficulty remaining?

 

[swraman]

Use Ampere's Law:
$$\oint B \bullet dl = \mu_{0}I$$

integrate around a closed circle of radius 8.5m centered around the wire. Since each infinitesimal point dl around the circle's circumfrence will have the same magnetic field passing through it (and because the B field is perpendicular to the circle at all points) the entire wire has the same magnitude of magnetic field passing through it.

So the integral reduces to:

$$B\oint dl = \mu_{0}I$$
$$B * 2 * \pi * r= \mu_{0}I$$
$$B = \frac{\mu_{0}I}{2 * \pi * r}$$

where r is the radius of the circle 8.5M and I is the current in the wire 95A.