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Chapter 28 Inductance; Magnetic Energy Storage

Chapter 28 Inductance; Magnetic Energy Storage. Self inductance. Electric current. magnetic field. EMF. (changing). (changing). Phenomenon of self-induction. Magnetic flux Φ B ∝ current I. L is self inductance of the coil. Unit: Henry (H). 2. EMF of inductor.

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Chapter 28 Inductance; Magnetic Energy Storage

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  1. Chapter 28 Inductance; Magnetic Energy Storage

  2. Self inductance Electric current magnetic field EMF (changing) (changing) Phenomenon of self-induction Magnetic flux ΦB∝ current I L is self inductance of the coil. Unit: Henry (H) 2

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

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

  5. R1 R2 1 Inductance of coaxial cable Example1: Determine the inductance per unit length of a coaxial cable with thin conductors. Solution: Magnetic field ? Ampere’s law: I I 5

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

  7. Mutual inductance (1) For two coils near each other I1 changes → EMF in coil 2 Total flux in coil 2 created by current I1: M21 is the mutual inductance of coil 2 with respect to coil 1, depends on geometry & ferromagnetics 7

  8. Mutual inductance (2) I2 changes → EMF in coil 1 It can be proved that: The unit of mutual inductance is also Henry (H) How to determine the mutual inductance? 8

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

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

  11. Two coils Example3: Determine the mutual inductance of two ideal coupling coils (L1, L2). Solution: Current I1 in coil 1: 11

  12. Current I2 in coil 2: Combine with: Discussion: 1) Generally: 2) Total inductance? (connect 2 and 3) Connect 2 and 4? 12

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

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

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

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

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

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

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