For a coil of radius r with N turns and current I, the field on the axis at distance x is proportional to N I r squared divided by (x squared + r squared) raised to three by two.

• At the centre, x becomes zero and the axial formula reduces to the maximum centre field for the loop.
• The field decreases non-linearly with x and tends to zero far from the loop, so the graph is not a straight-line decay.
• Trap: using 1 over x squared or 1 over x directly for every off-centre point without checking the exact axial expression.

At the centre, a full loop gives the standard maximum field, while an arc gives only the angle fraction of that full-loop value. Concentric loops add or subtract depending on current direction.

• A semicircle contributes half the full angular factor, and a three-quarter arc contributes three-fourths of the full circular contribution.
• For concentric coplanar loops, same-direction currents reinforce the field and opposite-direction currents oppose it.
• Trap: forgetting that current distributed across the diameter produces zero field at the centre because opposite elements cancel there.