Sketch of the system geometry and variables. The sensor is in the -plane and has an active area with side lengths and in the - and -directions, respectively. The origin of the coordinate system is in the center of the sensor. The bias current is uniformly distributed and runs from to .
Values of the normalized average magnetic field from a single bead placed at for a square sensor and (increasing values indicated by arrow). Part (a) shows the results as function of for and part (b) shows the results as function of for . The insets show the sensor geometry and the investigated values of and are indicated by the dashed lines.
Maximum average magnetic field relative to that for a bead placed at the center [Eq. (11) ] as a function of for a square sensor. The inset shows the position of the maximum as function of .
Cross-section of part of sensor (gray bar) with magnetic beads placed at with , 0.5, 1, and 1.5. The magnitude and direction of the bead dipole vectors induced by the self-field are indicated by the arrows. The curves show the -component of the field from each of the beads observed on the sensor at . The dashed parts of the curves are outside the sensor area and do not contribute to the average.
Values of for beads distributed on the active area of a square sensor and (×) for an infinite monolayer of beads over the sensor as a function of . The lines are the indicated simple analytical approximations. The inset shows and for high values of .
Values of (a) and (b) calculated as a function of as described in the text. The lines are the analytical approximations valid for low values of described in the text.
Contours in percent of the cumulative bead signal on a sensor covered with a half-space of homogeneously distributed beads with .
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