Transcript
Page 1: Capacitors with Dielectrics

Capacitors Capacitors with with

DielectricsDielectricsAP Physics C

Montwood High School

R. Casao

Page 2: Capacitors with Dielectrics

Dielectric

• A dielectric is a nonconducting material inserted between the plates of a capacitor.

• A dielectric increases the ability of a capacitor to store energy.

• If the dielectric completely fills the space between the plates, the capacitance increases by a factor k, called the dielectric constant.

dAεk

C o

Page 3: Capacitors with Dielectrics

Dielectric•When a dielectric is inserted between the plates of a charged capacitor that is not connected to a battery (a source of additional charge), but the voltage is reduced by a factor k.

new

old

VV

k

Page 4: Capacitors with Dielectrics

Dielectric

• Since the charge Q on the capacitor does not change, then the capacitance must change with the changing voltage so that the charge remains constant.

• The capacitance increases by a factor k when the dielectric completely fills the space between the plates.

• The dielectric constant is a measure of the degree of dipole alignment in the material.

old

new

CC

k

Page 5: Capacitors with Dielectrics

•From the equation for capacitance

the capacitance can be increased by decreasing the distance d between the plates.•The value of d is limited by the electrical discharge that could occur through the dielectric medium separating the plates.•For any separation d, the maximum voltage that can be applied across the capacitor plates without causing a discharge depends on the dielectric strength of the dielectric.

dAεk

C o

Page 6: Capacitors with Dielectrics

•In other words, the maximum electric field the dielectric material can withstand without allowing a transfer of charge between the plates is the dielectric strength.•If the electric field strength in the dielectric exceeds the dielectric strength, the insulating properties will break down and the dielectric material begins to conduct. This is called dielectric breakdown.

dV

)E(ds dielectric

Page 7: Capacitors with Dielectrics

•“Polarization” of a dielectric in an electric field E gives rise to thin layers of bound charges on the dielectric’s surfaces, creating surface charge densities +i and –i.

Page 8: Capacitors with Dielectrics

An Atomic Description of Dielectrics

(a)Polar molecules are randomly oriented in the absence of an external electric field.

(b)When an external field is applied (to the right as shown), the molecules partially align with the field; the dielectric is now polarized.

Page 9: Capacitors with Dielectrics

(a) When a dielectric is polarized, the dipole moments of the molecules in the dielectric are partially aligned with the external field Eo. (b) This polarization causes an induced charge on the opposite side. This separation of charge results in a reduction in the net electric field within the dielectric.

The net effect on the dielectric is the formation of an induced positive surface charge density ind on the right face and an equal negative surface charge density –ind on the left face.

Page 10: Capacitors with Dielectrics

The induced surface charge give rise to an induced electric field Eind in the direction opposite the external field Eo.

Page 11: Capacitors with Dielectrics

What is the Magnitude of the Induced Charge Density?

Note that the induced charge density on the dielectric is less than the charge density on the plates.

For parallel plate capacitor,

External field Eo = /o

Induced Field Eind = ind/o

and E = Eo/k = /k·o

Substitute into E = Eo - Eind gives

;

1

ind ind

o o o o o o

o oind

o o

ind

k k

k k

k kk k k

Page 12: Capacitors with Dielectrics

Dielectrics

Page 13: Capacitors with Dielectrics

• The net electric field in the dielectric is given by: E = Eo - Einduced

• The dielectric provides these advantages:• Increases the capacitance of the capacitor.• Increases the maximum operating voltage of

a capacitor.• May provide mechanical support between

the conducting plates.

new

old

E

Ek

Page 14: Capacitors with Dielectrics

Effect of the Dielectric Constant

odielectric

EE

k o

dielectric

EE d d

k

odielectric

VV

k

Potential difference with a dielectric is less than the potential difference across free space

oo

Q QC k k C

V V Results in a higher capacitance.

Allows more charge to be stored before breakdown voltage.

Page 15: Capacitors with Dielectrics

Effect of the Dielectric Constant

Parallel Plate Capacitor o oo o

A k AC C k C

d d

ok

AC

d

Material permittivity measures degree to which the material permits induced dipolesto align with an external field.

2 2 2o 0 0

1 1 1u E u k E E

2 2 2

Example modificationsusing permittivity

Page 16: Capacitors with Dielectrics

•The energy of the capacitor is lowered when a dielectric is inserted between the plates. Work is done on the dielectric.•A force must act on the dielectric which pulls it into the capacitor. •The nonuniform electric field near the edges of a parallel plate capacitor exerts this force.•The horizontal component of the electric field acts on the induced charges on the surface of the dielectric, producing a horizontal force directed into the capacitor.

Page 17: Capacitors with Dielectrics

• Place a dielectric material between capacitor plates:• A charge of -13 is on the right

negative plate of the capacitor.• A charge of +7 is on the right

positive portion of the dielectric.• The battery sees -13 + 7 = -6

(less total charge on the negative capacitor plate).

• To compensate for the absence of charge, the battery sends more charge to the negative capacitor plate to restore the -13 charge.

• This is how a dielectric allows for more charge to be stored on the capacitor plates.

Page 18: Capacitors with Dielectrics

Effect of a Metallic Slab Between the Plates

A parallel-plate capacitor has a plate separation d and plate area A. An uncharged metallic slab of thickness a is inserted midway between the plates.

Page 19: Capacitors with Dielectrics

Charge on one plate must induce a charge of equal magnitude but opposite sign on the near side of the metallic slab.

Net charge on the slab is zero, electric field inside the slab is zero.

Capacitor = two capacitor in series, each having a plate separation of (d-a)/2 as shown.

Page 20: Capacitors with Dielectrics

1 2

1 1 1 1 1 1;

2 21 2 1 2 1 1

; ;2

21

;

o oT T

o o oT T T

oT

T o

A AC C C Cd a d a

A A AC C Cd a d a d a

Ad aC

C A d a

Page 21: Capacitors with Dielectrics

Effect of a Metallic Slab between the plates

What are the differences in the result as compared to the previous example if we insert the metallic slab as shown?

Page 22: Capacitors with Dielectrics

A Partially Filled Capacitor

A parallel-plate capacitor with a plate separation d has a capacitance Co in the absence of a dielectric. What is the capacitance when a slab of dielectric material of dielectric constant k and thickness d/3 is inserted between the plates as shown.

Page 23: Capacitors with Dielectrics

A Partially Filled Capacitor

Two capacitors in series

1 21 2

1 1 1; ;

23 3

1 1 1

23 3

1 1 13 3

21 2

3 3

1 23 3

31 2;

3 (1 2 )

o o

T

o oT

o oT

T o o

T o o

oT

T o

k A AC C

d dC C C

k A ACd d

k A ACd dd d

C k A A

d k dC k A k A

k Ad k dC

C k A d k

Page 24: Capacitors with Dielectrics

Two Dielectric Slabs• Consider a parallel-plate

capacitor that has the space between the plates filled with two dielectric slabs, one with constant k1 and one with constant k2.

• The thickness of each slab is the same as the plate separation d and each slab fills half the volume between the plates.

• The two different dielectric slabs represent two capacitors in parallel with a plate area A/2.

Page 25: Capacitors with Dielectrics

Two Dielectric Slabs

1 2

21

1 2

1 2

2 2

2( )

2

T

ooT

o oT

oT

C C C

k Ak AC

d dk A k A

Cd

A k kC

d

Page 26: Capacitors with Dielectrics

Charge Storage Warning

• Capacitors can store a charge for a long time after the power to them has been turned off. This charge can be dangerous.• A large electrolytic capacitor charged to

only 5 V or 10 V can melt the tip of a screwdriver placed across its terminal.

• High voltage capacitors like those in TV’s and photoflash units can store a lethal charge.

• Technicians ground themselves to avoid electric shock.


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