《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 9 Magnetic Fields：II

Chapter 9 Magnetic Fields: II Ampere' s circuital law Example: Long Cylindrical Conductor Example: Toroidal Coil Example: Refraction of Lines of b at a Current sheet Short solenoid The curl of b

Chapter 9 Magnetic Fields:II ◼ Ampere’s Circuital Law ◼ Example:Long Cylindrical Conductor ◼ Example:Toroidal Coil ◼ Example:Refraction of Lines of B at a Current Sheet ◼ Short Solenoid ◼ The Curl of B

9. 1 Ampere's circuit Law It is known that near a long straight wire the magnetic induction is 1 B 2丌 P1 so over a circle of radius p centered on the wire(see g9-1) ∮B·dl 丌p=10 Figure 9-1 Positive direction for the ntegration path around a current L

T his is a general result for any closed curve C B Note the right-hang screw rule here for the directions of B and i This can be generalized to the ampere's law For a volume distribution of current B·dl=p0sJda, where j is the current densi ity thro h ugh any surface s bounded by the curve C See Fig 9-2 a

C B

In many cases the same current crosses the surface bounded by the curve C several times See Fig. 9-2(b)for a solenoid Then the total current isⅠ×N, C

In many cases the same current crosses the surface bounded by the curve C several times. See Fig. 9-2(b) for a solenoid. Then the total current is I×N