Magnitude of the magnetic field produced by a wire

In summary, the magnitude of the magnetic field produced by the power line is calculated using Ampere's Law and is equal to \mu_{0}I/2 * \pi * r. This value can be compared to the Earth's magnetic field of about 1/2 G.
  • #1
Kiyah
1
0

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[tex]\mu[/tex]/2[tex]\pi[/tex]I/r

The Attempt at a Solution


4[tex]\pi[/tex]e-7/2[tex]\pi[/tex]95/8.5
 
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  • #2
The formula is not appearing quite right on my screen, but you clearly have the right one. Is there any difficulty remaining?
 
  • #3
Use Ampere's Law:
[tex]\oint B \bullet dl = \mu_{0}I[/tex]

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 teh 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:

[tex]B\oint dl = \mu_{0}I[/tex]
[tex]B * 2 * \pi * r= \mu_{0}I[/tex]
[tex]B = \frac{\mu_{0}I}{2 * \pi * r}[/tex]

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

1. What is the formula for calculating the magnitude of the magnetic field produced by a wire?

The formula for calculating the magnitude of the magnetic field produced by a wire is B = (μ0 * I) / (2 * π * r), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current in the wire, and r is the distance from the wire.

2. How does the direction of the current affect the magnitude of the magnetic field produced by a wire?

The direction of the current does not affect the magnitude of the magnetic field produced by a wire. The strength of the magnetic field is determined by the current and the distance from the wire, regardless of the direction of the current.

3. How does the distance from the wire affect the magnitude of the magnetic field produced?

The magnitude of the magnetic field produced by a wire decreases as the distance from the wire increases. This relationship follows an inverse-square law, meaning that the magnetic field strength is inversely proportional to the square of the distance from the wire.

4. What is the unit of measurement for the magnitude of the magnetic field produced by a wire?

The unit of measurement for the magnitude of the magnetic field produced by a wire is the Tesla (T). It can also be measured in Gauss (G), with 1 T = 10,000 G.

5. How can the magnitude of the magnetic field produced by a wire be increased?

The magnitude of the magnetic field produced by a wire can be increased by increasing the current in the wire or by decreasing the distance from the wire. Additionally, using a material with a higher permeability, such as iron, can also increase the strength of the magnetic field.

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