Calculate inverse-distance magnetic fields and combine wire contributions.
Method and worked examples
Near a long straight wire, the field magnitude is B=(2πr)μ0I, where μ0≈4π×10−7TmA−1 in the stated approximation. Thus B=r2.00×10−7I with SI units. The distance is perpendicular to the wire. Unlike the point-charge electric field, this field varies as r1 rather than r21. The long-wire expression becomes less accurate near wire ends.
Find the direction of each wire’s field at the point before combining magnitudes. Equal parallel currents produce opposing fields at their midpoint; equal opposite currents produce reinforcing midpoint fields. Elsewhere, use signed collinear components or perpendicular vector addition. A graph of B against I at fixed r is linear, while a graph of B against r1 at fixed I is linear under the model.
Example 1
A long wire carries 5.00A. Find B at 0.0200m using μ0=4π×10−7.
B=2.00×10−7×0.02005.00=5.00×10−5T.
Example 2
At a point, wire fields are 30.0μT east and 40.0μT north. Find magnitude.
B=√30.02+40.02=50.0μT=5.00×10−5T.
Watch out:The ideal long-wire field is inversely proportional to perpendicular distance, B ∝ r1.
7. Fields of straight wires and superposition | Year 12 Physics | Ascent Arcade