Magnetic force of two parallel wires is inverse proportional to distance?

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SUMMARY

The magnetic force between two parallel wires is inversely proportional to the distance between them, following the formula F = (μ * I * I2) / (2π * r). This relationship is primarily a 2-dimensional problem, where the force behaves as 1/r. As the distance increases, particularly beyond 1 km, the force approaches an inverse square relationship (1/r²). Understanding these distinctions is crucial for accurately predicting magnetic interactions in various dimensional contexts.

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  • Understanding of magnetic force principles
  • Familiarity with the formula for magnetic force between parallel wires
  • Basic knowledge of dimensional analysis in physics
  • Concept of inverse relationships in physics
NEXT STEPS
  • Study the derivation of the magnetic force formula for parallel wires
  • Explore dimensional analysis in electromagnetic theory
  • Investigate the effects of distance on magnetic force in different dimensions
  • Learn about the applications of magnetic forces in real-world scenarios
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Physics students, electrical engineers, and anyone interested in the principles of electromagnetism and magnetic interactions between conductors.

ctech4285
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Its right.

The inverse X laws are different in different dimensions. Two infinite parallel wires is a lot like a 2-D problem where its usually the "inverse-r" law.
 
ah that makes sense, thanks! 1d -> r; 2d -> 1/r; 3d -> 1/r`2
 
To complete your 3D understanding of this, imagine two wires 1km long separated by 1cm.

For these wires, as they are separated the force will go very nearly as 1/r. When they are about 1km apart it will not be 1/r or 1/r^2 but something in between. When they are a million km apart the force will go very nearly as 1/r^2.

(1D goes as a constant or 1/r^0)
 

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