Chapter 9 Magnetic Fields: Il 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 B 2Tp so over a circle ot radIus p centered on the wire(see g1) ∮B·dl 2丌 Figure 9.1 positive direction for the integration path around a current 1
This is a general result for any closed curve c lc B dI=uo ote the right-hang screw rule here for the directions of B and i This can be generalized to the ampere s law or a volume distribution of current 欠B.dl=0sJ·da, where J is the current density through 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 is IXN
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