Magnetism: Magnetic force between wires

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SUMMARY

The discussion focuses on calculating the magnetic field intensity at a point equidistant from two long parallel wires carrying equal antiparallel currents of 8 Amperes, separated by a distance of 1 cm. The initial calculation of the magnetic field intensity (B) was incorrectly performed using the dot product instead of the cross product, leading to an erroneous result. The correct approach involves recognizing that the magnetic field from each wire is perpendicular to the radial vector, which affects the resultant magnetic field calculation. Ultimately, the correct magnetic field intensity at point P is approximately 3.192e-5 T.

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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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It looks like you got the angles wrong. Don't forget that the magnetic field from each wire is perpendicular to the radial vector.
 
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.
 

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