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Prof. David R. Jackson ECE Dept.

ECE 2317 Applied Electricity and Magnetism. Spring 2014. Prof. David R. Jackson ECE Dept. Notes 29. Mutual Inductance. I 2. I 1. Two coils are in proximity of each other. . Current reference directions and unit normals are defined on both coils.

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Prof. David R. Jackson ECE Dept.

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  1. ECE 2317 Applied Electricity and Magnetism Spring 2014 Prof. David R. Jackson ECE Dept. Notes 29

  2. Mutual Inductance I2 I1 Two coils are in proximity of each other. Current reference directions and unit normals are defined on both coils. (The unit normals are each determined from the corresponding current reference directions, by the right-hand rule.)

  3. Mutual Inductance (cont.) I1 21 Coil 1 is energized Coil 2 is left open-circuited Define mutual inductance: (calculated when I2 = 0) Note: For the figure shown, 21<0 if I1 > 0. Hence M21< 0. In general, if coil 2 has multiple turns:

  4. Mutual Inductance (cont.) I2 12 Coil 2 is energized Coil 1 is left open-circuited Define mutual inductance: In general, if coil 1 has multiple turns,

  5. Mutual Inductance (cont.) A general property (proof omitted) is that both mutual inductance components are always equal:

  6. Circuit Law for Coupled Coils M L2 L1 i2 i1 v2 + - v1 + - Total flux through coil 2: Total flux through coil 1:

  7. Example R2 R1 z Ls= length FindM12 , M21 I1 I2 For M12: y Bz2 R1 x R2

  8. Example (cont.) R2 R1 z Ls= length I1 I2 For M21: y Bz1 R1 R1 x Note: Bz1= 0 for  > R1. R2

  9. Example (cont.) R2 R1 z Ls= length I1 I2 Summary

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