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Lecture 7.1 :!Electron Current

Lecture Outline:!More on Capacitors/Dielectrics!

The Electron Current!Creating Current!

Current and Current Density!!

Feb. 24, 2015

Textbook Reading:!Ch. 29.7 - 30.3

Announcements

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!

•HW6 due next Tue. (March 3) at 9am on Mastering Physics.!

•Quiz #3 in class this Thursday (Feb. 26). Will cover Ch. 29 material.!

•If you haven’t already done so, please fill out mid-semester evaluation forms. It’s anonymous, and it’s helpful to me.!

•Exam #1: Average = 66.5 ± 17.01 %!

•Questions? Concerns? Please feel free to e-mail me or drop by my office.

Last Lecture...

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1 farad = 1 F ≡ 1 C/V

C � Q

�VC

Capacitance is a geometric property!

C � Q

�VC=

�0A

d

�VC = Ed

UC =Q2

2C=

1

2C(�VC)

2

Energy Stored in a Capacitor.

Last Lecture...

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Capacitors in Parallel

Ceq = C1 + C2 + C3

Capacitors in Series

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Ceq=

1

C1+

1

C2+

1

C3

More on Capacitors

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What is the equivalent capacitance of this circuit?

Clicker Question #1

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A capacitor charged to 1.5 V stores 2.0 mJ of energy. If the capacitor is charged to 3.0 V, it will store

!

A. 1.0 mJ. B. 2.0 mJ. C. 4.0 mJ. D. 6.0 mJ. E. 8.0 mJ. UC ∝ (ΔV)2

Dielectrics

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So far we’ve assumed our parallel-plate capacitors are filled with vacuum (i.e. - nothing). What if we insert

some other material?

Capacitance = ?

Dielectrics

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Capacitor with no dielectric

Dielectric is polarized.

Electric Field is diminished.

Dielectrics

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� � E0

E

�VC = Ed =E0

�d =

(�VC)0�

C =Q

�VC=

Q0

(�VC)0/�= �

Q0

(�VC)0= �C0

Voltage diminishes

Capacitance Increases

Dielectric Constant

Dielectrics

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More on Capacitors

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Two 5.0 mm x 5.0 mm electrodes with a 0.1mm thick sheet of Mylar (κ=3.1) between them are attached to a 9.0 V battery.

At some time the Mylar is withdrawn. !What is the potential energy stored in the capacitor before/

after the Mylar is removed?!

The Electron Current

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We need to develop an understanding of how charges can move through systems.

Current = controlled motion of charge.

Charged Capacitor Discharged Capacitor

Wire

The Electron Current

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Electrons are the charge carriers in metals!

electron current (ie) = number of electrons per second that pass through a cross-section of wire.

The Electron Current

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How long does it take to discharge a Capacitor?

If drift speeds of ~10-4 m/s are typical, it would take an electron

2000 seconds to travel 20 cm. ????

Discharge doesn’t happen by moving electrons from one plate

all the way to the other!

Creating Current

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The fact that current is “flowing” implies the electrons must be subject to some force.

Electric field inside conductor is due to ends of conductor being at different potentials.

Creating Current

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Conduction electrons are like free particles moving through a metal lattice.

No Electric Field!Average Velocity is Zero

With Electric Field!Average Velocity is NonZero

Creating Current

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vx

Between collisions the acceleration is constant. Magnitude of the average velocity is called the drift speed, vd

Creating Current

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Acceleration in E-Field

Clicker Question #2

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A wire carries a current. If both the wire diameter and the electron drift speed are doubled, the electron current increases by a factor of!A. 2. B. 4. C. 6. D. 8. E. Some other value.

ie ∝ Aνd

Current and Current Density

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Electrons are the charge carriers in metals!

electron current (ie) = number of electrons per second that pass through a conductor in a given time.

ie = neA�d =nee⇥A

mE

Current and Current Density

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I � dQ

dt

Current was known long before electrons were discovered, so conventional definition of current is in terms of Charge:

1 ampere = 1 A ≡ 1 coulomb per second = 1 C/s

I =Q

�t=

eNe

�t= eie

Conventional current and electron current are related:

Current and Current Density

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By convention, current is defined to flow in the direction in which

positive charges would move! (i.e. - in the direction of the Electric Field)

Reminders

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!

•HW6 due next Tuesday (March 3)!•Quiz #3 this Thursday (Feb. 26)!•If you have any questions/concerns, please feel free

to e-mail me or stop by my office. !!