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+ Q free on inner surface. + + + + + + + + + + + +. - - - - - - -. - q bound. Symmetry – fields must be uniform – field lines perpendicular to plates. + q bound. + + + + + +.

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3805816

+Qfreeon inner surface

+ + + + + + + + + + + +

- - - - - - -

-qbound

Symmetry

– fields must be uniform

– field lines perpendicular to plates

+qbound

+ + + + + +

- - - - - - - - - - - -

-Qfreeon inner surface

Interior points electric

field must be zero


3805816

area of plates A

+ + + + + + + + + + + +

+Qfreeon inner surface

plate separationd

-Qfreeon inner surface

- - - - - - - - - - - -


3805816

+

+

+

+

+

conductor

-

-

-

dielectric

Gauss’s Law


3805816

dielectric

Constant

(polar

molecules)

frequency


3805816

Fme

dy

+ + + + + + + + +

+ + + + + + + + +

F

-

-

-

-

-

-

-

-

-


3805816

+ + + + + + + + + + + +

- - - - - - - -

+ + + + + + + +

- - - - - - - - - - - -

Electric field

Electric displacement

Polarization


3805816

only some of the windings are shown

A

Integration paths

B

C


3805816

L

Bz

Bz

dA1

dA2

Br

dA3


3805816

Z

Y

X


3805816

Bz1

Br = 0

Ienclosed = 0

I

A

Bz2

s

x


3805816

Bz1= 0

C

Br = 0

Ienclosed = nsI

I

Bz2

s

Ienclosed = 0

I

Bz1= 0

Bz2

x

x

x

x

x

x


3805816

single turn of wire with current I

B

around integration loop B

dr = 0 and Br = 0

outside loop Bz = 0


3805816

iron core

BFe HFe

gap region

Bgap Hgap

i

coil windings

Bair Hair


3805816

.

.

.

.

.

.

.

.

3

X

X

X

X

X

X

2

Current i

out of page

Circulation loop:

square of length L

1

4

Current i

into page

Cross-section through electromagnet


3805816

thickness t

width L

q = - e

area A

electrons are the charge

carriers in copper


3805816

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -


3805816

+ + + + + + + + +

dy

+ + + + + + + + +

F

- - - - - - - - -

-q

+q


3805816

C

+ + + + + + + + +

V

r

CA

CB

- - - - - - - - -

L-x

C = CA + CB

x


3805816

Induced dipole moment – helium atom

+2e

+2e

-e

-e

-e

-e

Zero electric field – helium atom symmetric  zero dipole moment

A

B

effectively charge +2e at A and -2e at B

dipole moment p = 2ed


3805816

Induced dipole moment – sulfur atom

+16e

+16e

-8e

-8e

-8e

-8e

Zero electric field – helium atom symmetric  zero dipole moment

A

B

effectively charge +16e at A and -16e at B

dipole moment p = 16ed


3805816

Er

E

P

r2  r + (d/2)cos

r1  r – (d/2)cos

r

(d/2)cos

+q

-q


3805816

dA

+f

+ + + + + + + + +

-b

+b

- - - - - - - - -

-f


3805816

-q

+q


3805816

S

+f

-b

O

r

+b

-f


3805816

Width of ring r d

Radius of ring r sin

+

+

+

Area of the shaded ring

between  and  + d

surface S

d

r

-

Pcos

-

-


3805816

+

+

+

electric field at O

due to charge dqe

E0 cos

E0

element of charge dqe

-

-

-


3805816

+Ze

+Ze

d

a

a

d << a


3805816

F

F

+Q

d

F

- Q


3805816

+ p E

U

0

- p E

π

π/2

0


3805816

U = - p E

Lowest energy state

U = 0

U = + p E

highest energy state

-

-

-

 = 90o

+

+

+

 = 0

 = 180o


3805816

r - 1

1/T


3805816

Po

T


3805816

1

slope = 1/3

0

10

pE/kT


3805816

Gaussian surface S

conducting

sphere q

air

a

r

non-conducting

liquid

Symmetry  field lines must be radial


3805816

conducting

sphere q

Eairt

air

Eliquidt

non-conducting

liquid

Symmetry  Eairt = Eliquidt Eair = Eliquid = E


3805816

field lines of E

field lines of D

+


3805816

field lines of D

+

+

+

+

+

+

+

+

+

+

greater concentration of charge

on surface bounded by liquid

field lines of E

+


3805816

-

+

+

-

-

+

+

shift in atoms

due to ionic nature of bond

induced dipoles due

to shift in electron cloud

rotation

orientation of polar molecules


3805816

6

5

4

S

N

HFe

Hair

Circulation loop: square side L

2

1

3


3805816

Cylindrical

Gaussian

surface

Gauss’s Law for magnetism

B-field lines –

form continuous loops


3805816

N pole

im

Bound surface currents im (right hand screw rule)

 


3805816

un-magnetized piece of iron

Bar magnet bought near

un-magnetized piece of iron

N

N

N

 Bar magnet will attract the iron that was initially un-magnetized

north pole attracts

south pole


3805816

Cu ramp

Fe ramp

plastic ramp

N

N

N


3805816

Circulation loop for circulation integration used in applying Ampere’s Law

N

N

Hair

Hiron


3805816

B

I

I

(0,0)

d

H

B

d


3805816

Miron

PERMANENT MAGNET

Hiron

B

B, Hgap

Mgap = 0

B = Bgap = Biron

ELECTROMAGNET

Miron

Hiron

B

Mgap = 0

B, Hgap

B = Bgap = Biron


3805816

Y

thickness t

area A = wt

width w

X

current in

X direction

Z

magnetic field in Z direction

Schematic diagram of a Hall Probe


3805816

width

w

Y

+ + + + +

- - - - -

_

VH

+

VH

- - - - -

+ + + + +

X

charge carriers electrons (-)

eg wire, N-type semiconductor

charge carriers positive (+)

eg holes in P-type semiconductor

I

.

Z direction

out of page


3805816

e-

-

e

length L

area

A

resistance R

resistivity 

conductivity 

number densityn

+

I

_

_

v

electron

V


3805816

e-

-

e


3805816

image

object

Z

A

electron beam

Y

X


3805816

+Z

Electron at A moving parallel to +Y-axis

vy

Electron acted upon by the radial component of the magnetic field  force on electron in +X direction  +X-component to the velocity

Fx

due to Bz

By

axis for the motion of the electron beam

+Y

Bz

radial component

of magnetic field

+X


3805816

+Z

Electron at B has a velocity component in the +X direction

Fy

due to Bz

Electron acted upon by the axial component of the magnetic field By force on electron in -Z direction i.e. towards to axis  focusing action

Fz

due to By

vx

By

axis for the motion of the electron beam

+Y

Bz

radial component

of magnetic field

+X


3805816

ifree

.

.

.

.

.

.

.

.


3805816

external magnetic field


3805816

Electrostatic

capacitor

Electrolytic

capacitor


3805816

Electrostatic capacitor

Electrolytic capacitor


3805816

Electrochemical double layer capacitor

d

conductive

electrode

conductive

electrode

separator

activated carbon


3805816

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-


3805816

+

+

-

Electric Field

-

-


3805816

+

Zero applied stress

-

Compressive stress

Induces a voltage

Applied voltage produces

An expansion


3805816

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

Ferroelectric material

Antiferroelectric material


3805816

Interior points electric

field must be zero

+0.2Q on outer surface

+

+

+ + + + + + + + + +

+Q on inner surface

- - - - - - - - - -

-Q on inner surface

Interior points electric

field must be zero

Symmetry

– electric field must be uniform

– electric field lines perpendicular to conductive plates


3805816

Symmetry

– fields must be uniform

– field lines perpendicular to plates

Interior points electric

field must be zero

+ + + + + + + + + +

+Q on inner surface

- - - - - - - - - -

-Q on outer surface

+ + + + + + + + + +

+Q on outer surface

-Q on inner surface

- - - - - - - - - -

Interior points electric

field must be zero


3805816

Electric field between

Adjacent plates

+q

-q

-q

+q

+q

-q

+V


3805816

...

...

...

V

Capacitors in series (charge on each plate)

Capacitors in parallel (voltage across each capacitor is the same)

Series

branch


3805816

Capacitors in parallel

-Q1

+Q1

C1

Q =Q1+Q2

+Q2

-Q2

Ceq = C1+C2

C2

V

V

Capacitors in series

Q

+Q

-Q

1/Ceq = 1/C1+1/C2

-Q

+Q

C1

C2

V

V


3805816

air

fuel

fuel

w

l

h


3805816

+Q

- +

r

Induced dipole


3805816

a

Slab 1

a

a

5a

Slab 2

a

a


3805816

S1

S3

S2

S4


3805816

+ Q

+ Q

- Qb1

C1

- Q

+ Qb1

- Qb2

+ Qb2

+ Q

- Q

C2

- Q

Capacitors in series


3805816

E = 0


3805816

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

E = 0

-

-

-

-

-

-

-

-


3805816

+Q/2

+Q/2

C1 = Q / 2V1

C1

C1

V1

Q = 2 C1V1

- Q/2

- Q/2

qA = C2V2 = r C1 V2

qB = C1 V2

Q = qA + qB

= C1 V2 (r + 1)

= 2 C1 V1

V2 = 2 V1 / (r + 1)

qA = 2 C1 V1 r / (r + 1)

qB = 2 C1 V1 / (r + 1)

+qA

+qB

V2

C1

C2

- qA

- qB


3805816

+Qf

-Qf


3805816

+q

d

t

r

- q


3805816

Homogenous dielectric – uniformly polarized

Dielectric is neutral

+

+

+

+

+

+

+

-

-

-

-

-

-

-

The electrical field is reduced in the dielectric material


3805816

+

+

+

+

+

+

+

+

+

+

+

Thin long rod L = 0

Zero polarization

Sphere L = 1/3

Concentration of charges

At surface given by

-

-

-

-

-

-

-

-

-

-

-

Flat plate L = 1

Max polarization


3805816

+ Q

- Q


3805816

+

Q

-

Q

b

1

E1

+

Q

b

1

-

Q

b

2

E2

+

Q

b

2

-

Q


3805816

R1

R2


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