1 Chapter30 Inductance

• Self-inductance or Inductance: a changing current i in any circuit causesa self-induced emf.

• Self-induced emf

ε = −LdIdt

(1.1)

where L, inductance of device; SI units: H (Henry)

L = NdφBdI

= NφBI

(1.2)

For solenoid

L == NφBI

= NBAcosθ

I= Nµ0nIA =

µ0N2A

l(1.3)

For toroidal solenoid

L = NφBI

= NBAcosθ

I= N

µ0Ni

2πr

A

I=µ0N

2A

l(1.4)

Example 30.3, 30.4

• Mutual-inductance: when a changing current i1 in one circuit causes achanging flux in a second circuit, an emf ε2 is induced in the secondcircuit.

M is mutual inductance.

ε2 = −M di1dt

(1.5)

ε1 = −M di2dt

(1.6)

M =N2φB2

i1=N1φB1

i2(1.7)

1

1.1 Energy stored in a magnetic field

U =1

2LI2 (1.8)

U =1

2C(∆V )2 (1.9)

Magnetic energy density in vacuum u = B2

2µ0

1.2 RL circuits

Figure 30.12

ε− IR− L∆I

∆t= 0 (1.10)

Current growth

I =ε

R(1 − e−t/τ ) (1.11)

Current decay

I =ε

Re−t/τ (1.12)

1.3 LC circuits

Graph30.14Angular frequency of oscillation

ω =

√1

LC(1.13)

2

1.4 LRC series circuits

Underdamped: if R is relatively small, the circuit oscilates with damped har-monic motion.

ω =

√1

LC− R2

4L2(1.14)

Damped circuit: R is big

3