Announcements

Reminders:

No lectures next week: Feb 15th and Feb 17th

Quiz II: March 3rd, Ch 25,26, most of 27. {tentative}

Exam Grades

Median: 85.5 % {high B+}Mean: 82.8% {low B+}

Stdev: 13.2%Questions: email or ask in office hrs

Exam Histogram

Exam Score distribution

02468

1012

95 90 85 80 75 70 65 60 55 50 45 40

Scores

Nu

mb

er

Exam Comments

Most Common issues:

Field does NOT depend on the magnitude of the test charge, but does on the distance.

The force from a field on a charge depends on the sign of the charge.

Not all oscillatory motion is simple harmonic motion!

On each exam, there should be: Score, Exam Grade

Overall Grade

The overall grade is what you would have now. If thereare two grades this indicates that you are at an interface.

Capacitor•Two conductors carrying charges of equal magnitude but opposite sign form a capacitor.

+Q-Q

A parallel plate capacitor is a particularly common type:

+Q -Q

Capacitors have a voltage across them

Capacitor: Field Lines

+q -q

Perfect parallel plate capacitors have a uniform field. And of course a potential difference

Capacitors and Charge

•Capacitors store charge•Capacitance is measure of how well it stores charge•Capacitance is a constant for a given capacitor.

•Farad (F) is C/V, the unit of capacitance

•Typical capacitances are in F or pF ranges.

Capacitors and Charge

•Capacitance is a constant for a given capacitor.

Q C V The voltage (i.e. potential difference) used is this equation is positive.

•C depends only on the geometry of the capacitor!•Note: the material doesn’t matter (except in between the plates}

•If I change the voltage (for a given geometry), I change the charge. If the charge changes, than the voltage must have changed

Finding Capacitance

ab

+Q-Q2

0

ˆ4

QE r

r

•So we need to find the field the find the voltage (use Gauss law, withthe sphere as the gaussian surface )

b

a

V E ds

QC

V

Finding Capacitance

ab

+Q-Q2

0

ˆ4

QE r

r

b

a

V E ds

204

b

a

Qdr

r

04

b

a

Q

r

04

Q b a

ab

Q

CV

04 abC

b a

Finding Capacitance: isolated sphere

ab

+Q-Q

04 abC

b a

a b

+Q-Q

•The isolated sphere is the limit as b-> infinity of the concentric spheres

aC o4ba

ao

1

4

A Parallel Plate Capacitor

d

area A

0 AC

d

0 AC

d

Dielectric constant

Circuits: First glancewire (conductor)

capacitor

switch

battery+–

We will learn how to combine these elements and others as the class progresses.

+–This is what is right here!

Batteries•An ideal battery creates a voltage difference between the two sides

+–

E

A battery can be used to charge a capacitor, and maintain a constantvoltage.

Combining Capacitorswire (conductor)

capacitor

switch

battery+–

In Series:C1 C2 C3

C1 C2 C3

In Parallel:1 2 3C C C C

1 2 3

1 1 1 1

C C C C

Same VoltagesVoltages are the same across each capacitor

Charges are the same on each capacitor

Each of the Capacitors above has a capacitance of 12 F. What is the combined capacitance of the whole system?

A) 12 F D) 36 FB) 6 F C) 4F

Combining Capacitors

Combining Capacitors•For complex problems, capacitors may be combined successively in pairs.

4 F

8 F

6 F

12 F6 F

4 8 12C

1 1 1

12 6C

3 1

12 4

4 FC

Each of the Capacitors above has a capacitance of 12 pF. What is the combined capacitance of the whole system?

A) 12 pF C) 8 pFB) 4 pF D) 20 pF

12 12 24C 12

12

12

12

1 1 1 3 1

12 24 24 8C

24812 8 20C