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Topic 5 (Electricity & Magnetism)

where we re-do the first 4 topics, but watch electric charge, rather than mass

Quiz 5 was Tue.Apr.03 . . . here is my grading key as *.jpg image

Electric charge comes in TWO kinds : Positive (protons) and Negative (electrons) ... the total is conserved !
=> q_object   =   N e   . . .   integer Number of "elementary charges" e

charge in motion   q v   is called Indicated Electric Current . . . (+)→ and ←(−) both are   I →
=> I = ΔQ / Δt   ~ ρ v A   ... 1 C/s is called an Ampere ... it is similar to momentum as mass flow

Electric charge is pushed or pulled by the Electric Field   E . . . like mass is pulled by a gravity field

Positive charges carry Electric Field that points outward, away from themselves
      in the direction that a (+) proton would be pushed .
. . . the Electric field intensity weakens with distance ... as 1/distance squared
      since the Electric field (out farther) spreads over a bigger surface Area (like a planet's Gravity field).
. . . negative charges carry Electric Field that points inward, toward themselves
      in the direction that a (+) proton would be pulled .
=> E = k Q /d ²   . . . k = Coulomb's constant = 9E9 Nm²/C² .

Electric Field extends through space from positive electric charge to negative electric charge

When we separate positive charges from negative charges, we stretch this Electric Field
. . . this puts Tension in the space between the charges
      this requires us to do Work ... which puts Energy in the new charge configuration
. . . we might think of it as moving one of the charges along the Electric field (that is caused by the other charge)
      the Electric Field points "downhill", toward lower PE for positive charge (analogous to gh in mechanical world)
      so if we move the positive charge away from the negative one, we move it "uphill"
=> W = F·d = (q E)·d = q (E·d) = q ΔV   . . . charge moved thru a difference in Potential

Electric field Units : 1 Newton/Coulomb = 1 Volt/meter

Electric Potential   V   is the environment part ("aspect") of Electric Potential Energy   q V

Positive charges are surrounded by positive Electric Potential   V
      so a proton nearby would have positive electric Potential Energy
. . . but an electron nearby would have negative electric PE
      electrons are usually trapped (with negative PE) in the electric PE well of their atom
      ... like planets are trapped in the Gravity PE well of their Sun.

Negative charges are surrounded by negative Electric Potential   V
      so a proton nearby would have negative electric Potential Energy
. . . but an electron nearby would have positive electric PE
      and could be pushed away, trading this (+) PE for (+) KE farther away.
=> PE_electric = q V   . . . 1 Joule = 1 Coulomb·Volt

here's a 2-dimensional graph of the Electric Potential (vertical axis)       near a positive charge (left) and a negative charge (right) everywhere on the left half has positive Potential . . . because it is closer to the positive charge       V = k Q / r the right side is closer to the negative charge . . . so the V there is negative V = 0 all along center-line , midway between the charges . . . there, the +V contributed by the positive charge       is cancelled by the −V that the negative charge contributes. => V contributions   add . . . it is a quantity describing the location (the environment there)

Power : the rate that charge carries Energy

A fresh battery has a lot of (+) PE because it has excess protons (+q) near the (+)V end,
      and also a lot of excess electrons (−q) near the (−)V end.
. . . in use, electrons leave the (−)V end with   (−e)(−V) = (+)PE,
      and eventually enter the (+) end with   (−e)(+V) = (−)PE .
It is the difference in potential (one end − the other) that is the voltage, which describes the "electrical landscape".
      the Electric Field is the gradient   (slope, distance-wise)   of the potential , so that's what determines how fast the charge flows.
. . . connect a really long wire to both sides of a battery, and the potential gradient along it will be very shallow, so very slow current
      connect that drop via a short route, and the current might be so fast as to melt its insulation off!
. . . if there are 2 routes from high PE to low PE, some charge will take each route ... more will take the steeper or wider wire
      the shorter wire with big Area conducts well , so it presents low resistance to charge flow.
. . . if there are 2 obstacles (light bulbs) in a path (from high to low), the 2 voltages ("electric height" drops) must add to be the total voltage
      current will flow ½ as fast (I = ½ I₁) because each bulb (filament length) can only be half as steep ... since their voltages add.
=> I = V /R   . . . where R is the Resistance to flow ... "obstacle-ness" ... Resistances in series add ... since the same current flows thru both bulbs!

sort-of-optional: more about electrical resistance

You may think of resistance as electric friction, transforming electric PE into Thermal TE
      the faster the current goes thru, the faster the Energy gets "lost to friction" ... since Power = ΔE/Δt ,
=> Power = I·V   . . . Watt = Amp·Volt .

resistance depends on the length of the conductor × how hard that kind of material is to go thru
. . . conductance ... 1/resistance ... depends on the Area that the electrons can go thru
=> R = resistivity * L / A . . . resistivity is a material property (look up in a table) but it changes with Temperature

Resistances in series add ... because their lengths add
      2 resistors in series exert 2× the resistance (to current flow) as one did
. . . resistances in parallel are reduced ... conductances in parallel add ... because their Areas add
      3 resistors in parallel exert 1/3 as much resistance as one did

moving charge is encircled by magnetic field ... magnetic field deflects moving charge

Magnetic Field exits a magnet's "North" pole , and enters a magnetic "South" pole

Opposite poles attract ; like poles repel
. . . a compass is a small bar magnet on a pivot;
      its magnetic North pole is labeled with "N" ... attracted to Magnetic South poles
. . . compass "N" points geographically Northward - toward Canada
=> "Magnetic South" pole is underneath Canada (magnetic North is below AntArtica)

Electric current flowing ccw around a coil makes a magnetic field
. . . magnetic field is most intense up thru the inside of the coil Area
      same number of loops down around the coil outside, but spread farther
. . . single current loop has one North face and one South face
      field looks just like a "button magnet" field
. . . second current loop in the same sense (cw/ccw) adds to that field
      (current loop in opposite sense cancels it)
. . . coil wrapped around iron core can be 100's of times as strong.

magnetic material contains atomic-scale current loops

If you break a magnet, and pull the 2 pieces apart,
. . . a new "South pole" and a new "North pole" appear in the middle.
. . . the "ends" of a magnet are not really the source for the Magnetic field
=> the entire magnetic material is the source for the Magnetic Field

each atom is a tiny magnet ... the valence electron orbits are most important
      but each proton is a magnet, each neutron is a magnet, each electron is a magnet)
. . . the electron's orbit axis can re-orient ... in a magnet, the orbits align along their neighbors' orbits
. . . their magnetic fields re-inforce one another ... add together constructively
      (c.f: when electric dipoles align, their Electric fields tend to cancel)
=> there is no such thing as an "isolated magnetic pole" ... always magnetic field pointing along an axis

Magnetic field intensity decreases with distance
      (as their field spreads, of course!)
. . . an object magnet will tend to turn ... when a subject magnet approaches
      so that its opposite pole is nearest the subject's approaching pole
. . . so magnets turn each other in a way that they will attract one another
      but the source dipole partly cancels, and the Force partly cancels
=> magnet-to-magnet Force goes as ~ 1/distance to the fourth
    so   magnets aligned oppositely will attract each other from the side
    and   magnets aligned alike will attract each other from either end.

electromagnet & motors & generators & transformers

generator: mechanical Energy input, turns a permanent magnet
. . . this pushes the (conduction) charges along a (wire) coil
      which "seem to be moving" , relative to the turning magnet
. . . while the magnetic pole tip sweeps across the coil material
      (that is, when their torque is maximum)
. . . the current flows from the coil carrying electric Power
      as (−) charge at (−) electric potential.
. . . some motors can also be used as a generator
. . . some generators can be used as a motor
=> "hybrid" cars can "brake" by having their magnets push charge into their batteries

transformer: a "generator" that uses an electro-magnet input, instead of a permanent magnet
. . . many-loop coil (input) makes intense magnetic field even with small current
      (its long wire impedes current, even if the voltage is high)
. . . few-loop coil at output has lots of current, even if not much voltage
      it is the number of loops that determines the voltage
. . . Power in ≈ Power out ; they are often over 90% efficient
      wall : 0.2 Amp · 120 Volt = 4 Amp · 6 Volt , at battery

a transformer requires changing current ... so they do not work with DC ...
. . . some DC-DC converters make their input current change
      by "switching" the input circuit on and off

here's a map of where the Magnetic South Pole has been . . . wandering around the North geographic (spin) pole       it has been moving much faster than usual, recently . . . it has been getting less intense, also recently       mostly because it seems to be fragmenting South pole and North pole "switch" routinely in the geologic record . . . on average, every half million years it is over-due to reverse again . . . since the last reversal was ¾ million years ago.