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Lecture 6.2 :!Capacitors

Lecture Outline:!Finding Field from Potential!Capacitance and Capacitors!Energy Stored in a Capacitor!

Dielectrics!

Feb. 19, 2015

Textbook Reading:!Ch. 29.3 - 29.7

Announcements

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•HW5 due next Tue. (Feb. 24) at 9am on Mastering Physics.!

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

•If you have Satvik Wani as your TA, and you don’t see a grade for your MidTerm #1 in Blackboard, you need to bring your exam to either him or me ASAP. Apologies for the hassle.

Last Lecture...

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V � Uq+sources

q

�V = �� f

i

�E · d�s

�U = �� f

i

�F · d�s

�E = �⇥V

Finding Field from Potential

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Clicker Question #1

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Which set of equipotential surfaces matches this electric field?

Stronger Fields = Closer Equipotentials!

Finding Field from Potential

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Kirchhoff’s Loop Law

Finding Field from Potential

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1. Electric Field inside is zero.!

2. Excess charge is on surface.!

3. Surface is equipotential.!

4. Interior is equipotential!

5. Exterior field is perpendicular to surface.!

6. Field and surface charge density are largest at sharp corners. (Why?)

Conductor in Equilibrium

Lightning Rods

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Capacitance and Capacitors

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Capacitors come in many shapes/sizes. Common elements in electrical circuits. “Caps”.

Capacitance and Capacitors

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Battery charging up a Capacitor

Capacitance and Capacitors

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E =Q

�0A

�VC = Ed

Q =�0A

d�VC

1 farad = 1 F ≡ 1 C/V

C � Q

�VC

Capacitance is a geometric property!

C � Q

�VC=

�0A

d

Clicker Question #2

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What is the capacitance of these two electrodes?

!A. 8 nF. B. 4 nF. C. 2 nF. D. 1 nF. E. Some other value.

Capacitance and Capacitors

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Capacitors in SeriesCapacitors in Parallel

Clicker Question #3

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Which arrangement has larger equivalent capacitance?

A. Left!B. Right!C. Both are equal

Parallel => add Series => inverse of sum of inverses

Energy Stored in a Capacitor

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dU = dq �V =q dq

C

UC =1

C

� Q

0q dq =

Q2

2C

UC =Q2

2C=

1

2C(�VC)

2

Incremental change in energy (dU) as charge (dq) is added.

Total Energy Stored

Rewriting in terms of Potential across Capacitor.

Energy Stored in a Capacitor

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A 10000 microFarad capacitor is charged to 36V. What is the energy stored inside this capacitor?!

If the capacitor discharges in 10 microseconds, what is the power dissipated?

Energy Stored in a Capacitor

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UC =1

2C(�VC)

2 =1

2

�0A

d(Ed)2 =

�02(Ad)E2

For a Parallel Plate Capacitor:

The energy of a charged capacitor is stored in the electric field!

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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Reminders

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•Show up for recitations! Make sure you attempt/study all recitation problems, even if you didn’t get to them during recitation.!

•HW5 due on Tuesday (Feb. 24) at 9am.!•Quiz #3 Thursday (Feb. 26)!!