Prof. D. Wilton ECE Dept. Notes 27 ECE 2317 Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston.

Mutual Inductance I1I1 I2I2 Two coils are in proximity of each other. Current reference directions and unit normals are defined on both coils (The unit normals are determined from the current reference directions, by the right-hand rule.)

Mutual Inductance (cont.)  21 I1I1 In general, if coil 2 has multiple turns Coil 1 is energized. Coil 2 is left open-circuited Define mutual inductance:

 12 I2I2 In general, if coil 1 has multiple turns, Define mutual inductance: Coil 2 is energized. Coil 1 is left open-circuited Mutual Inductance (cont.)

Property: Mutual Inductance (cont.)

Circuit Law for Coupled Coils + - v1v1 i1i1 + - v2v2 i2i2 M L1L1 L2L2 total flux through coil 1: total flux through coil 2:

Example Bz2Bz2 R1R1 Find M 12, M 21 L s = length R2R2 z R1R1 I2I2 I1I1

Example (cont.) Bz1Bz1 R1R1 R2R2 z R1R1 I2I2 I1I1

R2R2 z R1R1 I2I2 I1I1

Force on Wire charge: wire: q B v F B I dl F The contour C is in the direction of the reference direction for the current.

Example I2I2 I1I1 1 2 z h z = 0 z = L x Note: there is no self-force on wire 2 due to the magnetic field produced by the current on wire 2.

Example (cont.) F F