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Example: calculate the magnetic field at point P due to a thin straight wire of length L carrying a current I. (P is on the perpendicular bisector of the wire at distance a.) y P dB r a x z ds I x L ds is an infinitesimal quantity in the direction of dx, so
y P dB r a x z ds I x L
y P dB r look integral up in tables, use the web,or use trig substitutions a x z ds I x L
y P dB r a x z ds I x
y P dB r a x z ds I x When L, The r in this equation has a different meaning than the r in the diagram! or