Magnetism: Magnetic force between wires

In summary, the magnetic field intensity between two long parallel wires carrying equal antiparallel currents can be found using the formula B = (mu_0 * I) / (2 * pi * r), where mu_0 is the permeability of free space, I is the current, and r is the distance from the wire. However, it is important to take into account the correct angles and use the cross product instead of the dot product. Once this is corrected, the magnetic field intensity at the point P, equidistant from the wires, can be calculated correctly.
  • #1
vsage
Magnetism: Magnetic field between wires

Two long parallel wires are a distance of d = 1 cm apart and carry equal antiparallel currents of 8 Amperes. Find the magnetic field intensity (in T) at the point P which is equidistant from the wires. (R = 10 cm).

This should be easy but I haven't gotten it right so far (as if that means it's hard). Here's what I did

[tex]B_1 = \frac{\mu_0i_i}{2\pi r_1}[/tex]
[tex]B_1 = \frac{2\times 8}{\sqrt{0.1^2+0.005^2}}[/tex]
= 1.598e-5 T roughly. Multiplied this by 2 since equal currents/radii in both wires. Vertical components cancel so I multiplied by [tex] \frac{0.1}{\sqrt{0.1^2+0.005^2}}[/tex] to get 3.192e-5 T. Where did I go wrong?
 

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  • #2
It looks like you got the angles wrong. Don't forget that the magnetic field from each wire is perpendicular to the radial vector.
 
  • #3
Yeah thanks I figured that out a few minutes after I posted but forgot to mention that little detail. What was I thinking?! Used the dot product instead of the cross product. Whoops.
 

Related to Magnetism: Magnetic force between wires

1. What is magnetism and how does it work?

Magnetism is a force that causes objects with magnetic properties to attract or repel each other. It is caused by the movement of charged particles, such as electrons, within a material.

2. How is the magnetic force between wires calculated?

The magnetic force between two wires can be calculated using the equation F = (μ0 * I1 * I2 * L) / (2π * d), where μ0 is the permeability of free space, I1 and I2 are the currents in the wires, L is the length of the wires, and d is the distance between them.

3. What factors affect the strength of the magnetic force between wires?

The strength of the magnetic force between wires is affected by the currents in the wires, the distance between the wires, and the permeability of the material between the wires.

4. Can the magnetic force between wires be increased?

Yes, the magnetic force between wires can be increased by increasing the currents in the wires or decreasing the distance between them. Additionally, using materials with higher permeability can also increase the force.

5. How is magnetism used in everyday life?

Magnetism is used in many everyday devices, such as speakers, motors, and generators. It is also used in credit cards, MRI machines, and compasses. Magnetism is also used in industries such as manufacturing, transportation, and energy production.

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