The homework assigned on Tuesday will not be due until Thursday, March 5.

Forces Acting on Dielectrics

More charge here

We can either compute force directly(which is quite cumbersome), or use relationship between force and energy

F U

Considering parallel-plate capacitor 2

2

CVU

Force acting on the capacitor, is pointed inside,hence, E-field work done is positive and U - decreases

2

2xU V C

Fx x

x – insertion length

Two capacitors in parallel

0 01 2 w( ) w

KC C C L x x

d d

w – width of the plates

20w

( 1)2x

VF K

d

constant force

Electric Current

Charges in Motion – Electric Current

Electric Current – a method to deliver energy

Very convenient way to transport energyno moving parts (only microscopic charges)

Electric currents is in the midst of electronic circuits and living organisms alike

Motion of charges in electric fields

const)(2

:conserved isenergy total thet,independen- timeis When

),( :motion ofEquation

/ :onAccelerati

:particle aon Force

2

2

2

r

E

rEr

Fa

EF

qmv

tqdt

dm

m

q

Motion in a uniform electric field

changenot do of componentsOther 2

)(

)(

/

:components-For

2

00

0

v

attvxtx

atvtv

mqEa

x

Deflection by a uniform electric field

ify

ifx

i

v

l

m

qEv

vv

xy

tm

qEy

tvx

y trajectorParabolic :

22

2

Application: Cathode Ray Tube

Electric Current in Conductors

In electrostatic situations – no E-field inside

There is no net current. But charges (electrons) still move chaotically, they are not on rest.

On the other side, electrons do not move with constant acceleration.

Electrons undergo collisions with ions. Aftereach collision, the speed of electron changes randomly.

The net effect of E-field – there is slow netmotion, superimposed on the random motion

6

4

~ 10 /

~ 10 /

chaotic

drift

V m s

V m s

Direction of the Electric Current

A

IJ

dt

dQ

Δt

ΔQIA

:areaunit per current theisdensity Current second 1

Coulomb 1Ampere 1 :Unit

: surfacethrough

charge of flow of rate with theassociated is Current in a flash light ~ 0.5 A

In a household A/C unit ~ 10-20 A

TV, radio circuits ~ 1mA

Computer boards ~ 1nA to 1pA

Current, Drift Velocity, Current Density

2[ / ]

Concentration of mobile charge

carriers per unit volume:

Average speed in the direction

of current (drift speed):

For a variety of charge carriers:

| |

d

d

d

di ii

Q qnAv t

I QJ qn v A m

A A t

n

v

J q n v

Current density J, is a vector while total current I is not

I d

J S

Electric current in ionic solution of NaCl is due to both positive Na+ and negative Cl- charges flow

Example: An 18-gauge copper wire has nominaldiameter of 1.02 mm and carries a constant currentof 1.67 A to 200W lamp. The density of free electronsis 8.5 X 1026 el/m3. Find current density and drift velocity

6 22

42 10 /

I IJ A m

A d

4; 1.5 10 /d dJ nev v m s

Why, then, as we turn on the switch, light comesimmediately from the bulb?

E-field acts on all electrons at once (E-fieldpropagates at ~2 108 m/s in copper)

Current density J and electric field E are established inside a conductor when a potential difference is applied –

Not electrostatics – field exists inside and charges move!

In many materials (especially metals)

over a range of conditions:

J = σE or J = E/

is the E-independent resistivity

σ=1/is the conductivity

This is Ohm’s law

(empirical and restricted)

Ohm’s Law

Conductors, Insulators and Semiconductors

(T) = 0[1+(T-T0)]

Resistance of a straight wire

1 ( )

Resistance

1 VoltUnit: 1 Ohm ( )

1 Ampere

1Resistivity

Unit: 1 m

b a b a

VI J A E A A

L

I V V V VR

LR

A

LR

A

V=IR

Water Flow Analogy

Interpreting Resistance

ohmic

(linear)

nonohmic

(non-linear)

I-V curves

Resistivity and Temperature

(T) = 0[1+(T-T0)]

Electrical Shock

“It’s not the voltage but the current.”

The current is what actually causes a shock - human body has resistance of ~500,000 with dry skin - ~100 wet! Requires conducting path.

Can cause: (1) burning of tissue by heating, (2) muscle contractions, (3) disruption of cardiac rhythms.

Current (A) Effect

0.001 Can be felt

0.005 Is painful

0.010 Causes spasms

0.015 Causes loss of muscle control

0.070 Goes through the heart - fatal after more than 1 second

– EVA Suit Specified to –40 V• anodized coating arcing occurred

at –68V in MSFC test– Possible Sneak-Circuit

• 1 mA safety threshold

Safety Tether

Display and Control Module (DCM)

Body Restraint Tether (BRT)

Mini Work Station (MWS)

Surface of spacesuit could charge to high voltage leading to subsequent discharge.

Discharge to the station through safety tether:• Tether is a metallic cable - connected to astronaut via non-conducting (nylon) housing.• Station maintained at plasma potential

- arc path closed when tether getswrapped around astronaut.

Metal waist and neck rings and other metal portions of the suit make contact with the sweat soaked ventilation garment providing possible conducting path for discharge through astronaut’s thoracic cavity.

Charging on Astronaut Space Suit in Auroral Zone: Potentially hazardous situation

Radial current leakage in a coaxial cable

€

J(r) =I

2πrL

V = E(r)dr =a

b

∫ ρJ(r)a

b

∫ dr =ρI

2πLln

b

a

R =ρ

2πLln

b

a