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 (I1): dt I d M

• I

M Φ

1 21 2 1 21 2

   E M21 is called the mutual inductance between the two loops. Mutual inductance is a pure geometric parameter, and its unit is Henry (H). s s A V H     

Mutual Inductance II

d d 4 M

2 1 21

r        Mutual inductance is a pure geometric parameter: From this it is clear that: M M

12 21

Self Inductance

dt dI L

• I

dt d

• I

B dt d

• emf

Back

L L B B L

           

L is called the inductance. SI unit of L : Henry (H)

Inductor

A N

• r

nNA L I dt d nNA

• nNAI

dt d

• emf

Back nNAI I)A n N( NBA I n B

2 L B

                  

B I

Inductor symbol: L



Capacitor and Inductor Capacitor C Inductor L Charge Q Current I E field B field

Parallel plate capacitor (uniform E field) Solenoid (uniform B field)

C Q V  t d I d L

• 



d V E and d A C    nI B and nNA L    

Energy Stored in a Capacitor

2

CV 2 1 U  V Q C 

Energy stored in a charged capacitor:

C

(Do not forget .)

E

Volume  =Ad

d Area A

Energy density stored in an electric field:

2 E

E 2 1 U u    

From Class 16

Energy Stored in an Inductor

2

LI 2 1 U  dt dI L

• 



Energy stored in an inductor:

L

(Do not forget .) Energy density stored in an electric field:

2 B B

B 2 1 U u    

Capacitor and Inductor Capacitor C Inductor L Charge Q Current I E field B field

Parallel plate capacitor (uniform E field) Solenoid (uniform B field)

C Q V  t d I d L

• 



d V E and d A C    nI B and nNA L    

2 E 2 E

E 2 1 u and CV 2 1 U   

2 B 2 B

B 2 1 u and LI 2 1 U   