1

Physics 1E3 Test Monday, Feb. 8

Time: 7:00 to 8:20 MDCL 1110, 1309.

Conflicts: e-mail your instructor.

.

• Capacitors in circuits • Electrostatic potential energy

Practice: chapter 26, problems 17, 21, 23, 33, 37

Text sections 26.3—26.5

2

Why use dielectrics in capacitors?

1)  the capacitance is increased by a factor κ 2)  the dielectric material gives mechanical strength

(holds the conductors apart) 3)  the plate separation can be smaller (which also

increases capacitance) 4)  the “dielectric strength”, or maximum electric field

before conduction starts, can be higher than for air, allowing higher voltage ratings

Quiz Two charged plates with charges +Q, -Q are suspended a distance d apart in a beaker of oil (dielectric constant = 2). The force one exerts on the other is

a)  the same as if they were in air b)  larger c)  smaller

3

Conducting spheres and a long wire:

A total charge +12 μC is placed on one sphere. Some of the charge will move to the other sphere until

A)  the electric fields on the spheres are equal B)  the electric potentials on the spheres are equal C)  the electric charges on the spheres are equal D)  all of the above

is smaller in many materials than it would be in a vacuum, for the same arrangement of charges.

Eg. Parallel plates:

(“kappa”) = “dielectric constant”

= (a pure number ≥ 1)

So, eg… (parallel plates)

4

Material κ

Vacuum 1 (definition)

air 1.0006

glass ~4 – 6

polystyrene 2.6

water 80

For any geometry,

i.e. Replace “ε0” with “ κε0 ” in the formulae.

Quiz Two charged plates with charges +Q, -Q are suspended a distance d apart in a beaker of oil (dielectric constant = 2). The force one exerts on the other is

a)  the same as if they were in air b)  larger c)  smaller

What if we compared plates in oil and air with the same potential difference, rather than with the same charge?

5

Symbols:

or

Capacitor

Battery

Switch

+ + - -

A B

Series

A B

Parallel

What is the “effective capacitance” between A & B?

A B

Q Q

6

C1 C2 C3 A

B

+Q

-Q

V Q1

-Q1

Q2

-Q2

Q3

-Q3

Voltages are the same: V1 = V2 = V3 = … = V

Charges add:

But…

Voltages add:

Charges are equal:

And …

Q +Q -Q +Q -Q +Q -Q +Q

7

a b

c d

All Capacitors are

Find the capacitance between a) points b and d. b) points a and d.

a b

c d

All Capacitors are

The capacitance between points b and d is

A) 12µF B) 6µF C) 2.4µF D) 24µF E) 60µF

8

a b

c d

All Capacitors are

Find the capacitance between a) points b and d. b) points a and d.

4 plates, each of area A, are connected as shown. What is the capacitance between B and D?

A) ½ ε0A/d B) ¼ ε0A/d C) 1/3 ε0A/d D) 3 ε0A/d E) 4 ε0A/d

d

d

d

D

B

9

d

d

d

4 plates, each of area A, are connected as shown.

What is the capacitance between B and D?

D

B

+q -q

dq Remove dq from lower plate and add to upper plate:

Increase in P.E.,

Start at q = 0, finish at q = Q:

10

Parallel-Plate Capacitor: and

Volume between plates

“Energy density”

(Units: J/m3)

We can think of this energy as stored in the electric field set up when the capacitor is charged:

This also applies to any electric field.

s

Area A +Q

-Q

Calculate:

a)  between plates

b)  between plates

c)  C between plates

d)  U of the system

e)  Force exerted on top plate (tricky...)

11

Quiz Two charged plates with charges +Q, -Q are suspended a distance d apart in a beaker of oil (dielectric constant = 2). The force one exerts on the other is

a)  the same as if they were in air b)  larger c)  smaller

What if we compared plates in oil and air with the same potential difference, rather than with the same charge?

Remains constant

Remains constant

From chap. 8:

Force by field on plate:

12

Find the capacitance between a and b.

a

b Solution:

Cs

a

b

(1)

(2)

x

d

w

L

Dielectric

A dielectric is slid into the space between the plates of a charged capacitor. What happens?

A)  The energy stored in the capacitor increases B)  The energy stored in the capacitor decreases C)  No change

+Q

-Q

13

What is the direction of the electrostatic force on the dielectric?

+Q

-Q

What is the magnitude of this force?

A)  The energy stored in the capacitor increases B)  The energy stored in the capacitor decreases C)  No change

What happens if we leave the battery connected?

x

14

x

d

w

L

-Q

+Q

Dielectric,

Find: 1) P.E. in capacitor as a function of x.

2) Force on dielectric due to field of capacitor.

a b

A neutral conductor of thickness a is slid between the plates of a parallel-plate capacitor (area A, separation b). What is the capacitance between the upper and lower plates?