Electric currents & Electromagnetism Micro-world Macro-world Lecture 9

Electric currents Micro-world Macro-world Lecture 9 (Motion of electric charges)

Alessandro Volta

Positive Ions _ _ _ _ Atoms with one or more electrons removed ”net” charge = + 2q e _ _ _ _

Battery C Zn Zn ++ - Zn ++ - Zn Zn Zn - + acid

“Voltage” Anode + Cathode E Zn ++ F W = Fd dF = 2q e E W = 2q e Ed  W 0 = 2q e E 0 d  =E 0 d W 0 2q e V “Voltage”

Anode + Cathode F=QE W = Fd E0E0 Q F=QE 0 Q =Q E 0 d = QV d Zn ++ Energy gained by the charge

Units again! W = Q V V = WQWQ joules coulombs  joules coulomb = Volt 1 V = 1 joule coulomb

Continuous charge flow = “electric current” Anode + Cathode Zn ++ QQ Electrical “conductor” connected between anode & cathode

electric current Anode + Cathode Zn ++ QQ I = Q t Units: Coulombs second =Amperes

The conductor can be a piece of wire Anode + Cathode Zn ++ I = Q t + + +

The energy can be used to run a gadget Anode + Cathode Zn ++ P= Energy time QV t == I V I I I

Electric light 60 Watts I=? T Power = P = I V I = PVPV = 60 W 100V = 0.6 J/s J/C = 0.6 1/s 1/C = 0.6 CsCs = 0.6 A V=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’ 1 st batteries

Christian Oersted

Electric currents produce B-fields I B

Right-hand rule B

Current loop NS

Two current loops N S

Even more loops N S

Solenoid coil Looks like a bar magnet S N

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 same direction: wires attract B

Forces on two parallel wires I I Current in opposite directions: wires repel B

Force law of Biot & Savart I2I2 I1I1 F =  B I1I2 ldI1I2 ld l d  = 2 x NA2NA2

Biot & Savart example 20A F =  B I1I2 ldI1I2 ld 2m 0.01m F = 2 x NA2NA2 20A (20 A ) 2 2 m 0.01 m F = 2 x N Small, but not tiny

Electric motor I B F I F

I B

Speakers Permanent magnet Solenoid Electro- magnet

Lorentz force B +q v i=qv F F = iB = qvB if v  B: direction by the right-hand rule

Electromagnetism Michael Faraday Faraday’s Law

Moving a Conductor in a B-field separates + & - 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 ┴ = A coil   = maximum B

Rotating coil in B field A ┴ = 0 (again)   = 0 B

AC voltage

Lenz’ Law v v B B + + N S the fall produces an induced current the B-field produced by the induced current tries to impede the fall B-field from induced current I

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 + 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 NA2NA2   ”strength” of magnetic force  2k  Wave speed =  2x9x10 9 Nm 2 / C 2 2x10 -7 N/A 2 =  9x (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 wave s radio wave s TV/FM AM