Class 39 Mutual and self inductance Mutual Inductance I Changing - PowerPoint PPT Presentation

Class 39 Mutual and self inductance

Mutual Inductance I Changing current in loop 1 will induce an emf in loop 2. Since the flux through loop 2 (  2 )is proportional to the current in loop 1 (I 1 ): d I    E Φ M I - M 1 2 21 1 2 21 dt M 21 is called the mutual inductance between the two loops. Mutual inductance is a pure geometric parameter, and its unit is Henry (H). V      H s s A

Mutual Inductance II Mutual inductance is a pure geometric parameter:      d d  M 0 1 2 21  r 4 From this it is clear that: 21  M M 12

Self Inductance d     Back emf - L B dt    B I B d dI      - I - L L L dt dt L is called the inductance. SI unit of L : Henry (H)

Inductor  I B   B n I 0       NBA N( n I)A nNAI B 0 0 d Inductor symbol:     Back emf - nNAI L 0 dt d   - nNA I 0 dt L 2 N     L nNA or A 0 0 

Capacitor and Inductor Capacitor C Inductor L Charge Q Current I E field B field Q d I V    - L C d t Parallel plate capacitor (uniform E Solenoid (uniform B field)   A V     field) L nNA and B nI  0 C and E 0 0 d d

Energy Stored in a Capacitor From Class 16 C Energy stored in a charged capacitor: 1 U  2 CV 2 Q C  (Do not forget .) V d Energy density stored in an electric field: U 1    2 Area A u E E E 0  2 Volume  =Ad

Energy Stored in an Inductor Energy stored in an inductor: L 1 U  2 LI 2 dI   - L (Do not forget .) dt Energy density stored in an electric field: U 1   2 B u B B   2 0

Capacitor and Inductor Capacitor C Inductor L Charge Q Current I E field B field Q d I V    - L C d t Parallel plate capacitor (uniform E Solenoid (uniform B field)   A V field)      L nNA and B nI C 0 and E 0 0 d d 1 1 1 1    2 2 U CV and u E   2 2 U LI and u B E E 0 2 2 B B  2 2 0