A V-shaped wire

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

Details and assumptions

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