I was trying to solve this problem and even I have solution I don't like it. So maybe you guys can share different approaches or (integration tricks)?
My solution (wrong):
Define angle θ between unit radial vector and a vector alone the wire. Then Bio-Savart law:
dB = μ/4pi ∫ dl sinθ/r^2, I should integrate this from α < θ < β
From the geometry x/r = sinθ, so r = sinθ/x.
Now i need to express dl in terms of θ, and this is where I may be wrong by assuming dl = -r dθ.
By continuing I do not get sensible answer. Any ideas?
My solution (wrong):
Define angle θ between unit radial vector and a vector alone the wire. Then Bio-Savart law:
dB = μ/4pi ∫ dl sinθ/r^2, I should integrate this from α < θ < β
From the geometry x/r = sinθ, so r = sinθ/x.
Now i need to express dl in terms of θ, and this is where I may be wrong by assuming dl = -r dθ.
By continuing I do not get sensible answer. Any ideas?
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