1. Chapter 28 Inductance; Magnetic Energy Storage

2. Self inductance 2 Magnetic flux Φ B ∝ current I Electric currentmagnetic fieldEMF (changing) Phenomenon of self-induction L is self inductance of the coil. Unit: Henry (H)

3. EMF of inductor 3 1) L shows the electromagnetic inertia of a coil A coil with significant L: inductor EMF induced in a inductor: 2) L depends on: geometry & ferromagnetics 3) Inductor in AC circuit → reactance / impedance

4. Determine inductance 4 For a long solenoid: Total magnetic flux: Self inductance: How to avoid inductance for a resistor?

5. Inductance of coaxial cable 5 Example1: Determine the inductance per unit length of a coaxial cable with thin conductors. Solution: Magnetic field ? 1 R1R1 R2R2 II Ampere’s law:

6. Inductance of toroid 6 Question: Determine the inductance of a toroid (N loops) with rectangular cross-section.

7. Mutual inductance (1) 7 M 21 is the mutual inductance of coil 2 with respect to coil 1, depends on geometry & ferromagnetics For two coils near each other I 1 changes → EMF in coil 2 Total flux in coil 2 created by current I 1 :

8. Mutual inductance (2) 8 The unit of mutual inductance is also Henry (H) I 2 changes → EMF in coil 1 It can be proved that: How to determine the mutual inductance?

9. Straight wire and coil 9 Solution: First determine M Example2: A long straight wire and a square coil lie in the same plane. If the current in coil is, what is the EMF on straight wire? Suppose current I in straight wire:

10. 10 How to minimize the mutual inductance? EMF on straight wire: Minimize Φ B : 1 2

11. Two coils 11 Solution: Current I 1 in coil 1: Example3: Determine the mutual inductance of two ideal coupling coils (L 1, L 2 ).

12. 12 Current I 2 in coil 2: Combine with: Discussion: 1) Generally: 2) Total inductance? (connect 2 and 3) Connect 2 and 4?

13. Magnetic energy storage 13 Current carrying inductor stores magnetic energy Storing energy in a rate: Energy stored in an inductor:

14. Energy in the field 14 How does magnetic energy distribute? Energy per unit volume / energy density:

15. Straight wire and coil 15 Solution: Example4: Determine the total energy stored in the toroid (N loops with current I )

16. Challenging problem 16 Show that by using the expression of magnetic energy stored in two coils.

17. *LR circuits 17 How does current I change? Time constant Reaction time for a inductor

18. *LC circuits 18 How does current I change? It’s a SHM!