# “…and then there was light.” Physics 100 Chapt 16 James Clerk Maxwell.

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“…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 + x E + E Is the change in E instantaneous? Does it occur only after some time? M.E.s can tell us?

fun in the bathtub Water level will increase but not instantaneously 1 st waves will propagate from her entrance point to the edge of the tub

According to Maxwell’s eqs: + x E + E The change in E is not instantaneous 1 st waves made of E- fields & B-fields propagate thru space.

Wave solutions to Maxwell’s Eqs: F c = k q1q2r2q1q2r2 k = 9.0 x 10 9 Nm 2 /C 2 k  ” strength” of electric force F M =  I1I2 ldI1I2 ld  = 2 x 10 -7 NA2NA2   ”strength” of magnetic force  2k  Wave speed =  2x9x10 9 Nm 2 /C 2 2x10 -7 N/A 2 =  9x10 9+7 (m 2 /C 2 )xA 2 =  9x10 16 m 2 /s 2 = = 3x10 8 m/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 - + - + + -

antenna E B

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 -6 m 4.0x10 14 Hz Green 0.55x10 -6 m 5.5x10 14 Hz Violet 0.4x10 -6 m 7.5x10 14 Hz Ultra- violet Infra- red X-rays  -rays micro waves radio waves TV/FM AM

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