Dielectrics

PH 203

Professor Lee Carkner

Lecture 9

Test 1 on Monday Covers the whole course through today

Chapters 21-25 10 multiple choice (20 points) 4 problems (20 points each) Equations and constants given

but not labeled Bring calculator

No PDA’s, no cellphones, no sharing Study

PAL’s Notes Homework

Other Capacitors

We can find C by solving V = ∫ E ds for a path between the plates

If we do this we find: Capacitance only depends on the geometry

of the plate arrangement (and

Cylinder

For a capacitor made from two coaxial cylinders, the area is 2rL and thus E = q/(20rL)

Integrating yields:

C = (20)[L / ln (b/a)] Where “ln” is the natural log, a is

the radius of the inner cylinder and b is the radius of the outer

Sphere For a capacitor made from

two concentric spherical shells, the area is 4r2 and thus E = kq/r2

C = (40)[ab/(b-a)]

Note for a single sphere:

Where R is the sphere radius

Between the Plates

In our treatment of the capacitor we assumed the space between the plates was filled with air

Each material has a dielectric constant, , that is multiplicative factor in the capacitance

C = 0A/d

Dielectric

The polarized material partially cancels out the electric field between the plates reducing the voltage

A dielectric allows a capacitor to store more charge with the same voltage

Dielectric Constant The dielectric constant is always greater than one

It is the number of times greater the capacitance is

compared to the air filled case

e.g. if we add a capacitor with = 2 we double the capacitance and the charge stored for a given voltage

Prevents “shorting out”

Breakdown The dielectric must be an insulator

If the voltage is large enough, the charge will jump across anyway

While Q = CV, there is a limit to how much we can increase Q by increasing V

When the voltage is too high and the capacitor shorts through the dielectric, it is called breakdown

Dielectric Strength

The field between the plates however depends on the voltage applied and the plate separation, d

E = V/d

Decrease the voltage Increase the plate separation

Energy in a Capacitor

Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch

Charge stops moving when the V across the plates is equal to the V of the battery

Charging a Capacitor

Total Energy

Energy = 1/2 Q V =1/2 C (V)2 = Q2/2C since Q = C V

Large C and large V produce large stored energy

Next Time

Test #1 For next Wednesday

Read 26.1-26.3 Problems: Ch 26, P: 1, 6, 13, 15

Three identical capacitors are connected in parallel. If a total charge Q flows from the battery, what is the charge on each capacitor?

A) Q/3

B) Q

C) 3Q

D) 6Q

E) 9Q

Consider two capacitors in series with a battery, two capacitors in parallel with a battery and a lone capacitor connected directly to a battery. If all the capacitors and batteries are identical, which ranks the situations from most to least charge stored?

A) Series, lone, parallel

B) Parallel, series, lone

C) Lone, series, parallel

D) Parallel, lone, series

E) Series, parallel, lone

If two capacitors are in series and a third capacitor is added in series, what happens to the total charge stored?

A) It goes up

B) It goes down

C) It stays the same

D) It depends on the C value of the new capacitor

E) It depends on the voltage of the battery