•Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ...

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Apr 1 2002 Electricity and Magnetism • Reminder – RC circuits – Electric Breakdown Experiment • Today – Magnetism

Transcript of •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ...

Page 1: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Electricity and Magnetism

• Reminder– RC circuits– Electric Breakdown Experiment

• Today– Magnetism

Page 2: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

RC CircuitsVariable time constant τ = RC

RC

Vin

VC

Vin

t

Page 3: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

In-Class DemoVin

tVC

t

t

I

Page 4: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

In-Class DemoVin

tVC

t

t

I

Page 5: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

In-Class Demo

• Changes in R or C change τ• Large τ smoothes out signals• Sharp edges/rapid changes get removed

– high frequencies are suppressed

• RC circuits are low-pass filters

Page 6: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Experiment EB

• Electrical Breakdown– You have seen many examples

• Lightning!• Sparks (e.g. Faraday Cage Demo!)• Fluorescent tubes

– Study in more detail– Reminder: Ionization

Page 7: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Ionization

• Electrons and nucleus bound together

• Electrons stuck in potential well of nucleus

• Need energy ∆U to jump out of well

• How to provide this energy?

U

e- ∆U

Page 8: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Impact Ionization

e-Ukin > ∆U

E

• Define Vion = ∆U/q• Ionization potential

• One e- in, two e- out• Avalanche?E

Page 9: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Impact Ionization

e-(1)(2)

λmfp λmfp : Mean Free Path

E• To get avalanche we need:

∆Ukin between collisions (1) and (2) > Vion * e• Acceleration in uniform Field

∆Ukin = V2 – V1 = e E d12• Avalanche condition then

E > Vion /λmfp

Page 10: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Impact Ionization

How big is Mean Free Path?

(i) If Density n is big -> λmfp small

Effective cross-section

(ii) If size σ of molecules is big -> λmfp small

λmfp = 1/(n σ )

Page 11: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Impact Ionization

Avalanche condition E > Vion /λmfp = Vion n σ

Experiment EB: Relate E, Vion ,σ

Example: Airn ~ 6x1023/22.4 10-3 m3 = 3 x 1025 m-3

σ ~ π r2 ~ 3 x (10-10m)2 = 3 x 10-20 m2

Vion ~ 10 VNeed E > 3 x 1025 m-3 x 3 x 10-20 m2 x 10 V ~ 107 V/m

For V ~ 800 V: V = E d -> d = 800/107 m ~ 0.1 mm

Page 12: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Experiment EB

+-

V

V d

HVPS 1MΩ

1MΩ

Page 13: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnetism

• Magnets: Materials with ‘strange’properties

• Magnets have been known for thousands of years

• It took until end of 19th century to understand the theory of Magnetism

Page 14: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Magnetic Force• New Force between Magnets• Unlike Poles attract

SN

• Like Poles repel

SNF F

SN S NF F

Apr 1 2002

Page 15: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnets

• Permanent Magnets

SN

• Two poles (called ‘north’ and ‘south’)• Let’s look at some properties

Page 16: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnetic Force

• Magnets also attract non-magnets!

FIron nail

Page 17: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnetic Force

• New phenomenon• Magnets carry no net charge!• Although not understood, magnetic

phenomena have been used for a long time -> In-Class Demo!

Page 18: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Electric Dipole in Electric Field

Page 19: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Compass

• Freely rotating magnets point towards earth’s (magnetic) north pole

Page 20: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnetic Field

• Magnets align themselves with Magnetic Field– like Electric Dipoles in Electric Field

• What is the Source of the Magnetic Field?

Page 21: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Current and Magnet

Wire, I = 0 Wire, I > 0

SN

XSN

Page 22: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Source of the Magnetic Field

• No effect due to Static Charges• But: An Electric Current affects Magnet• Does Magnet affect Current?

Page 23: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnet and Current

FI

• Force on wire if I != 0• Direction of Force depends on Sign of I• Force perpendicular to I

WireF

Page 24: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Current and Current

I I I I

F F F F

Attraction Repulsion

Page 25: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Summary

• Observed Force between– two Magnets– Magnet and Iron– Magnet and wire carrying current– Wire carrying current and Magnet– Two wires carrying currents

• Currents (moving charges) can be subject to and source of Magnetic Force

Page 26: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Free Charges and Magnetic Field

+qB

v

FL

FL = q (E + v x B)

Lorentz Force

Facc = m v2/R = FL

-> R = m v/(q B)[B] = N/(A m) = T (Tesla)

Cyclotron Radius

Page 27: •Reminder - MIT OpenCourseWare...Apr 1 2002 Impact Ionization Avalanche condition E > V ion /λ mfp = V ion n σ Experiment EB: Relate E, V ion,σ Example: Air n ~ 6x1023/22.4 10-3

Apr 1 2002

Magnetic Field and Work

+qB

v

FL

FL = q v x B (for E = 0)