![]() Where in vacuum the magnetic field and the magnetic induction are related by B = μ 0 H (SI units) or B = H (Gaussian units). Historically, this is the case considered by Biot and Savart. Take a straight, infinitely long, conducting wire transporting the direct current i. The vector r having dimension length, Laplace's formula describes an Inverse-square law.įield B due to current i in infinitely long straight wire. In Gaussian units k = 1/ c (one over the speed of light). In SI units k is equal to μ 0/(4π)-the magnetic constant μ 0 divided by 4π-and μ 0 = 4π ×10 −7 N/A 2 (newton over ampere squared). The constant k depends on the units chosen. The piece of the wire contributing to the magnetic induction B can be seen as a vector of infinitesimal length d s and with direction tangent to the wire. ![]() The direct electric current i is constant in time. Where the magnetic induction is given as a vector product, i.e., is perpendicular to the plane spanned by d s and r. Magnetic induction d B at point r due to infinitesimal piece d s (red) of wire (blue) transporting electric current i.Īt point r the magnetic induction d B due to id s (see the figure on the right and note that for typographical reasons vector arrows are omitted in running text) is given by the following formula due to Laplace,
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