76-89 A

70-75 AB

61-69 B

55-60 BC

40-54 C

< 40 D

Results of Midterm II

Physics 202, Lecture 17Today’s Topics

Inductance (Ch 30) Reminder of Faraday’s and Lenz’s Laws Self Inductance Mutual Inductance

Energy Stored in B Field

LR Circuits

Review: Faraday’s Law of Induction Faraday’s Law in plain words: When the magnetic

flux through an area is changed, an emf is produced along the closed path enclosing the area.Quantitatively:

dt

dB

!"=#

A

B

θ

! •=" AB dB

conventional direction of ε

Note the - sign

Review: Lenz’s Law Lenz’s law in plain words: the induced emf always

tends to work against the original cause of flux change

Cause of dΦB/dt “Current” due to Induced ε will:

Increasing B generate B in opposite dir.Decreasing B generate B in same dir.

Relative motion subject to a force in oppositedirection of relative motions

The magnetic flux due to selfinductance is proportional to I:

The induced emf is proportionalto dI/dt:

When the current in a conducting device changes,an induced emf is produced in the opposite directionof the source current self inductance

Self Inductance

L: Inductance, unit: Henry (H)

Exercise: Calculate Inductance of a Solenoid

show that for an ideal solenoid:

(see board)

Reminder: magnetic field inside the solenoid (Ch 28)!

L =µ0N2A

l

Area: A

# of turns: N

Mutual Inductance For coupled coils: ε2 = - M12 dI1/dt

ε1 = - M21 dI2/dt

Can prove (not here):M12=M21=M

M: mutual inductance(unit: also Henry) ε2 = - M dI1/dt

ε1 = - M dI2/dt

Examples of Coupled Coils (Transformers)

Question: Why use iron core?

Energy Stored in a Magnetic Field

When an inductor of inductance L is carrying a currentchanging at a rate dI/dt, the power supplied is

The work needed to increase the current in an inductorfrom zero to some value I

Energy in an Inductor Energy stored in an inductor is U= ½ LI2

This energy is stored in the form of magnetic field:energy density: uB = ½ B2/µ0 (recall: uE= ½ ε0E2)

Compare: Inductor: energy stored U= ½ LI2 Capacitor: energy stored U= ½ C(ΔV)2

Resistor: no energy stored, (all energy converted to heat)

Basic Circuit ComponentsComponent Symbol Behavior in circuit

Ideal battery, emf ΔV=V+-V- =εResistor ΔV= -IR

Realistic Battery (Ideal) wire ΔV=0 (R=0, L=0, C=0)Capacitor ΔV=V- - V+ = - q/C, dq/dt =I

Inductor ΔV= - LdI/dt(Ideal) Switch L=0, C=0, R=0 (on), R=∞ (off)Transformer

Future TopicsDiodes,Transistors,…

rε

An inductor and are resistance constitute a LR circuit Any inductor has a resistance, R R could also include any other additional

resistance When the current starts to flow a voltage drop will

occur a the resistance and the inductance Once current stabilizes, reaches maximum of

LR Circuit

Exercise: Turn on LR Circuit

Apply Kirchhoff loop rule

!

I =V0

R(1" e

"t

L /R )

Exercise: Turn on LR Circuit (cont)

Note: the time constant is τ=L/RQuiz: What is the current when t=∞ ?

!

I =V0

R(1" e

"t

L /R )

Exercise: Turn off LR Circuit

Apply Kirchhoff loop rule

!

I = I0e"

t

L /R

Exercise: Turn off LR Circuit (cont)

Note: the time constant is τ=L/RQuiz: What is the current when t=∞ ?

!

I = I0e"

t

L /R