A V-shaped wire

Consider a V-shaped wire that has the following shape: it comes in at an angle of α\alpha below the positive x-axis, bends at the origin, and exits at an angle of α\alpha above the positive x-axis. It is known that for such a wire configuration the magnetic field at point (r,0)(-r,0) can be written as B(r)=C(r)tan(α2) B(r)= C(r) \tan(\frac{\alpha}{2}) where C(r) C(r) is a function of rr. Using this information, find the magnitude of the magnetic field in Teslas if α=45 \alpha= 45^{\circ}, the current is I=1 A I=1~\mbox{A} (flowing from below the x-axis to above), and r=1 cmr=1~\mbox{cm}.

Details and assumptions

  • μ04π=107 H/m\frac{\mu_{0}}{4\pi}= 10^{-7}~\mbox{H/m}
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