Chapter 7 Magnetostatic Field
Lecture by Qiliang Li
§7.1 Introduction
Ampere’s manuscript
Ampere’s experiment
analogy between electric and magnetic fields
§7.2 Biot-Savart’s Law
§7.2 Biot-Savart’s Law
• 𝐼𝑑𝒍 = 𝑲𝑑𝑆 = 𝑱𝑑𝑉
• K is surface current density
• J is the (volume) current density
What happens when it is an infinite long line?
§7.2 Biot-Savart’s Law
Example 7.1 The conducting triangular loop in Fig.
7.6(a) carries a current of 10 A. Find H at (0,0,5) due
to side 1 of the loop.
Solve:
α1 = 90o ,
cosα2= 2/sqt(ρ2+22)
=2/ 29
What is the
direction?
§7.2 Biot-Savart’s Law
Example 7.2 Find H at (-3, 4, 0) due to the
current filament shown in Fig. 7.7(a).
Solve: find the angles: α1 and α2 , determine aφ
𝒂𝝓 = 𝑠𝑖𝑛𝜃𝒂𝒙 + 𝑐𝑜𝑠𝜃𝒂𝒚
§7.2 Biot-Savart’s Law
Example 7.3 A circular loop located on 𝑥 2 +
𝑦 2 = 9, z=0 carries a direct current of 10 A along
𝒂𝝓 . Determine H at (0,0,4) and (0,0,-4)