Electric currents& Electromagnetism

Micro-world Macro-worldLecture 9

Electric currents

Micro-world Macro-worldLecture 9

(Motion of electric charges)

Alessandro Volta

Positive Ions

_

_

_

_

++++

+

Atoms with one or moreelectrons removed

”net” charge = +2qe

_

_

_

_

Battery

C ZnZn

ZnZn

ZnZn++ - -

Zn++ - -

Zn++- -+ +

Zn++- -+ +

Zn

ZnZn - -+ +

acid

“Voltage”Anode

+ ++ +

+ +

Cathode

-

- - - - -

EZn++

F

+ ++

- - -

W = FddF = 2qeE

W = 2qeEd W0 = 2qeE0d =E0dW0 2qe V

“Voltage”

Anode

+ ++ +

+ +

Cathode

-

- - - - -

F=QE0

+ ++

- - -

W = Fd

E0

Q F=QE0Q

=Q E0d = QV

d

Zn++

Zn++

Energy gained by the charge

Units again!

W = Q V

V = W Q

joules

coulombs

joules coulomb

= Volt

1 V = 1 joule coulomb

Continuous charge flow = “electric current”

Anode

+ ++ +

+ +

Cathode

-

- - - - -

+ ++

- - -

Zn++

Zn++

Q Q

Electrical “conductor” connected between anode & cathode

electric current

Anode

+ ++ +

+ +

Cathode

-

- - - - -

+ ++

- - -

Zn++

Zn++

Q Q

I = Qt

Units:Coulombssecond

=Amperes

The conductor can be a piece of wire

Anode

+ ++ +

+ +

Cathode

-

- - - - -

+ ++

- - -

Zn++

Zn++

I = Qt

+ ++

The energy can be used to run a gadget

Anode

+ ++ +

+ +

Cathode

-

- - - - -

+ ++

- - -

Zn++

Zn++

P= Energy

time

+ ++

QVt= = I V

I I I

Electric light

60 Watts I=?

T

Power = P = I V

I = P V = 60 W

100V

= 0.6 J/s J/C = 0.6 1/s

1/C

= 0.6 C s = 0.6 AV=100V

General circuit

12V

+ -

Appliance+ -

Energy source(device that separates+ & - charge)

I

I

analogy

Height ~ voltage

Pump ~battery

Amt of water flow ~ current

appliance

pond

pump

Voltas’ 1st batteries

Christian Oersted

Electric currents produce B-fields

I

B

Right-hand rule

B

Current loop

NS

Two current loops

NS

Even more loops

NS

Solenoid coil

Looks like abar magnet

SN

Atomic magnetism

+- I

B

Some atoms are little magnets

Permanent magnet-microscopic view-

Magnetic forces on electric currents

I

Another right-hand rule

I

Forces on two parallel wires

II

Current in samedirection:

wires attractB

Forces on two parallel wires

I

I

Current in oppositedirections:

wires repelB

Force law of Biot & Savart

I2I1

F =

B

I1I2 ld

l

d

= 2 x 10-7 NA2

Biot & Savart example

20A F =

B

I1I2 ld

2m

0.01m

F = 2 x 10-7 NA2

20A

(20A)2 2m0.01m

F = 2 x 10-3N

Small, but not tiny

Electric motor

IB

F

IF

Electric motor

I

B

Speakers

Permanentmagnet

SolenoidElectro-magnet

Lorentz force

B

+q

v

i=qv

F

F = iB = qvBif v B:

direction by the right-hand rule

Electromagnetism

Michael Faraday

Faraday’s Law

Moving a Conductor in a B-fieldseparates + & - charges

I

Use this to drive an electric circuit

+

+I

+

+

+

Moving wire loop in a B field

+

+

v

An electric current is“induced” in the loop

Either the magnet or the loop can move

+

+

v

an electric current is“induced” in the loop

Magnetic flux () thru a loop

= BA┴

Flux thru a coil of N loops

= N BA┴

Faraday’s law

change in N BA┴elapsed time

Induced voltage in a circuit = change in elapsed time

EMF =

“Electro-Motive Force”

Michael Faraday

Rotating coil in B field

A┴ = 0 =0

B

Rotating coil in B field

A┴ = Acoil = maximum

B

Rotating coil in B field

A┴ = 0 (again) = 0

B

AC voltage

Lenz’ Law

v v

B B

+ +N

S

the fall producesan induced current

the B-field producedby the induced currenttries to impede the fall

B-field from induced currentB-field from

induced currentI

Lenz’ law

An induced voltage always gives rise to an electric current that creates a magnetic field that opposes the influence that produced it.

Maglev trains

Maglev

Maxwell’s Equations

James Clerk Maxwell

“…and then there was light.”

Properties of E & B fields

• Coulomb’s law: E-field lines start on + charge & end on – charge

• Ampere’s law: B-fields are produced by electric currents

• Faraday’s law: Changing B-fields produce E-fields

• (un-named law): B-field lines never end

In equation form:

E-field lines start on +charges & end on - charges

B-field lines never end

E-fields are produced by changing B fields

B-fields are produced by electric currents

Maxwell

The previous equations, as written, are mathematically inconsistent with the conservation of electric charge. He found he could fix this by adding one more term:

B-fields are produced by changing E-fields

Maxwell’s equations

B-fields are produced by changing E-fields

Fields from an electric charge

+

xE

+

E

Is the change in Einstantaneous?

Does it occur onlyafter some time?

M.E.s can tell us?

fun in the bathtub

Water level will increase

but not instantaneously

1st waves will propagatefrom her entrance pointto the edge of the tub

According to Maxwell’s eqs:

+

xE

+

E

The change in Eis not instantaneous

1st waves made of E-fields & B-fields propagate thru space.

Wave solutions to Maxwell’s Eqs:

Fc = k q1q2

r2

k = 9.0 x 109 Nm2/C2

k ”strength” of electric force

FM = I1I2 ld

= 2 x 10-7NA2

”strength” of magnetic force

2k

Wave speed =

2x9x109Nm2/C2

2x10-7N/A2

=

9x109+7(m2/C2)xA2=

9x1016m2/s2=

= 3x108m/s Speed of lig

ht!!

“…let there be light.”

Maxwell’s equations have solutions that are waves of oscillating E- & B-fields that travel at the speed of light.

Faraday & Maxwell made the immediate (& correct) inference that these waves are, in fact, light waves.

EM waves

-

+-+

+

-

antennaE

B

antenna

E

B

Light wave

E-field

B-field

wave velocity

+

-

Light wave animation

E

B

Electro-magnetic “spectrum”

Visible light: freq (c/)

Red 0.75x10-6m 4.0x1014 Hz

Green 0.55x10-6m 5.5x1014 Hz

Violet 0.4x10-6m 7.5x1014 Hz

Ultr

a-vi

olet

Infr

a-re

d

X- rays

- rays

mic

ro

wav

esra

dio

wav

es

TV/F

M

AM