Electromagnetic Theory (v2) #18 The Biot-Savart Law

Instructor: Dr. Süleyman Burak ÇELİK

We open the magnetostatics chapter with the Biot-Savart law: the rule that tells us what magnetic field a steady current produces. Starting from a tiny current element I dl at distance R from a point P, we build the differential field dH, unpack the cross product, apply the right-hand rule, and extend the law to surface and volume current distributions. We then integrate along a finite straight conductor to get the angle-form result H = I/(4πρ)(cos α₂ − cos α₁) â_φ, and reduce it to the two cases you will use the most: a semi-infinite wire (H = I/4πρ) and an infinite wire (H = I/2πρ). Topics: Bridge from electrostatics to magnetostatics, the Biot-Savart formula (dH = I dl × â_R / 4πR²), direction via the right-hand rule, three current distributions (line, surface, volume), straight conductor general formula, two special cases: semi-infinite and infinite wires. Reference: Sadiku, Elements of Electromagnetics 7th Ed, Section 7.2