“…and then there was light.”

Physics 100

Chapt 16

James Clerk Maxwell

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 = kq1q2

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

light!!

“…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

Ult

ra-

vio

let

Infr

a-

red

X-

rays

- rays

mic

ro

wave

srad

io

wave

sTV

/FM

AM