Magnetism: Magnetic force between wires

AI Thread Summary
The discussion focuses on calculating the magnetic field intensity at a point equidistant from two parallel wires carrying equal antiparallel currents of 8 Amperes, spaced 1 cm apart. The initial calculations attempted to apply the formula for magnetic field strength but encountered errors in vector direction and component analysis. Participants noted the importance of recognizing that the magnetic field from each wire is perpendicular to the radial vector, leading to the need for a cross product rather than a dot product in calculations. After addressing these mistakes, the correct approach to find the magnetic field intensity was clarified. The conversation highlights common pitfalls in applying magnetic field equations in practical scenarios.
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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

B_1 = \frac{\mu_0i_i}{2\pi r_1}
B_1 = \frac{2\times 8}{\sqrt{0.1^2+0.005^2}}
= 1.598e-5 T roughly. Multiplied this by 2 since equal currents/radii in both wires. Vertical components cancel so I multiplied by \frac{0.1}{\sqrt{0.1^2+0.005^2}} 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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