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One common approach to computing the magnetic field produced by a filamentarycurrent-carrying coil is to approximate the coil as a series of straightsegments. The Biot-Savart field from each straight segment is knownanalytically. However, if the endpoints of the straight segments are chosen tolie on the coil, then the accuracy of the Biot-Savart computation is generallyonly second-order in the number of endpoints. We propose a simple modification:shift each endpoint off the coil in the outwards normal direction by an amountproportional to the local curvature. With this modification, the Biot-Savartaccuracy increases to fourth order and the numerical error is dramaticallyreduced for a given number of discretization points.

Computation of the Biot-Savart line integral with higher-order convergence using straight segments