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B.4 For wires along toroidal direction

For a curve along the toroidal direction, the line element dl in terms of the cylindrical basis is written as dl = Rdϕˆeϕ. Using Cartesian coordinate basis vectors, dl is written as

dl = Rdϕ (− sin ϕˆex + cosϕˆey).
(644)

Using Eq. (644) and (633), we obtain

|| ˆex ˆey ˆez || dl× (r− r′) = ||− Rd ϕsin ϕ Rd ϕcosϕ 0 || || (x− x′) (y− y′) (z − z′)||
(645)

 

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