» Syllabus

Topic 1 (Electric charge, Force, E-field)

Home-Work Set for Topic 1 :

PRACTICE QUESTION SUGGESTIONS ...( NOT for grading ...) from Young 9th edition (odd problem answers in the book)
format codes :
      bold : Basic Bread-and-butter ... you'd better know how to do `em
      Italic : Important Ideas In here ... at least read `em
      Underline : Understand the Underlying structure ... not just the answer

ch.17 conceptual quests 1,3,5,7,8, 9,10,11,12,13,14 ;
      multiple-choice 1,3,4,5,7,8,9,11,12,13(after it touches?),14(c.f. mc#5)
      problems 3,4,5(memorize m,μ,n,p,f; k,M,G,T),10(E=?),11,14,15,18,20,23(what if 20mm→200mm?),24,25,26,30
      . . . 32,33,37,38,39,40,42,43,45,46,47,48,49,50(c.f.p#48,p#52),53,54,55,57,58,60,61,63,64,66,71,73(150 N/C),76,77

1.(~17p.10) A small balloon covered with −550 [nano-Coulomb] charge experiences an upward 0.20 [N] Force when it is a foot (0.30 [m]) above a wand's ball.
. . . a) Compute the Electric field there (at the balloon) that pushes this balloon. . . . b) calculate the charge on the wand's ball that makes this E-field.
. . . c) what would be different if the balloon was 0.30 [m] below the ball? . . . d) but the balloon had positive +550[nC] charge? . . . e) and was .25[m] below the ball?

2. Treat a Boron atom as 5 protons at the origin, 2 electrons in a shell (radius 13.2[pico-meter] centered on the origin) ,
      2 more electrons in a shell (radius 105.8[pm] centered on the origin) and its outer electron at x= 211.6 pm.
. . . a) what's the total charge centered on the origin? . . . b) what Electric field do they cause at x= 211.6[pm]?
      . . . c) what Force does the outer electron feel? . . . d) what acceleration should it have there?

3. Read problem 45. We model a NaCl molecule as a di-pole with a Cl⁻ ion at (vertically) y=−50[pm] and a Na⁺ ion at y=+70[pm], in an E-field = 3E11 [N/C] (x =rightward).
. . . a) calculate the Force applied to the Cl⁻ ion . . . b) calculate the Force applied to the Na⁺ ion
. . . c) calculate the total torque (r×F) applied to the molecule . . . d) the molecule will rotate to be in what orientation?

4. Treat a hydrogen atom as an electron moving in a circular orbit around a proton, at a distance 52.9 [pm] ;
      in this model, the Electric Force causes the electron's mass to accelerate in a circle (−R·a_r = v·v )
. . . use data inside back cover to calculate the speed needed for the electron . . . b) compute the time taken for one electron orbit.

Physics II Topic 1 Summary

Big Idea #1 : Electric Charge - - - abbreviated   Q   or   q - - - - - -

#1.a: intrinsic object property , microscopically - - - - - - - - - - - - - -
. . . each proton has positive charge ; Q_proton = e , the "elementary charge unit"
. . . each electron has negative charge ; Q_electron = −e ; same magnitude as proton , but negative
. . . each neutron has zero total charge ... (positive inner core, negative outer shell)

1.b: additive quantity - - - - - - - - - - - - - -

. . . make sure you keep track of positive and negative signs ...
      => each atom has zero total charge ... +Ze in nucleus + −Ze) in electron cloud around it (Z is "atomic number")

1.c: conserved quantity - - - - - - - - - - - - - -
. . . can be moved around, but the total amount is always the same.
      static electricity charge is easily transferred as one material rubs another (different) material
      . . . google "triboelectric" (rule-of-thumb: soft polymers tend to collect electrons from harder silicates and proteins)
      in clouds, positive charge on colder ice crystals transfers to warmer snowflakes (depends on Temperature!)

1.d: quantized quantity - - - unit   [elementary charge] , abbeviated   [e] - - - - -
      each ion has an integer number of excess electrons (neg.ions) or deficit electrons (pos.ions)
. . . so every isolated object ("ion", not atom) has charge Q = N e , where N is an integer (±) ; no partial electrons.
. . . we treat electric charge as if it isn't an intrinsic property of macroscopic objects

Macroscopic Unit of electric charge (S.I. Laboratory) is the "Coulomb" . . . 1e = 1.6E-19[C]
. . . 1[C] = 6.25E18 e . . . a mole of protons would carry ≈ 96,000 [C] !
      typical lab-scale charge accumulations are pico-Coulomb (1E-12 [C]) or femto-Coulomb (1E-15 [C]) .

#2: Charge Q is Source of an Electric Vector Field ... Q is the active subject

Charge Exudes an Electric Vector Field - - - - - - - - - - - - - -
Nonzero Q changes the environment nearby ; Electric Field Vector surrounds it
      points away from positive charge ... points toward negative charge
. . . you might consider "k_CQ" as the source of all its Electric field ,
      to help distinguish (in your mind) the vector E from the scalar Q .
. . . you should also notice that the Electric field is a property of the environment , the 3-d space we live in
      (as opposed to Q , which is a property of a material subject (massive particle of matter)
. . . if all air molecules were removed from a container , but charge was near it, then it would not be really empty.

#2.a: Electric Vector Field Weakens as it Spreads from Source

Coulomb's Law : - - - - - - - - - - - - - -
strength of E is weaker at larger distances from Q_source ... as E-field spreads out
      => E = k_C·Q_source/r² (away) .
. . . r is the distance from the source charge Q to the place where the E-field is calculated
. . . k_C is "Coulomb's constant" :   8.99E9 [Nm²/C²]   =   1.438 [V·nm/e]

Every source charge (nearby) contributes to the field at some location ;
. . . "simply" add all the contributions as vector arrows (tail-to-tip). (sarcasm here ;-)
. . . a spherical shell of charge can be treated as if its total charge was concentrated at the shell center
      except that only source material from shells that are inside your location count (outside contributions cancel).

Continuous Field Line approach - - - - - - - - - - - - - -
We may instead represent the Electric Field as lines which diverge from positive Q (use # lines proportional to Q)
. . . where E is weak , drawn lines (spread over large Area) are far apart :
      the intensity (strength) of E-field is proportional to "density of lines" , or # lines piercing a "unit surface"
. . . the lines continue until they converge on a negative charge , where they end (# converging is proportional to −Q) ;
If the total Q showing (on the page) is NOT zero , assume −Q_total is "spread uniformly" at infinity.

#3: Charge q is Forced by Electric Vector Field ... q is the passive object

Electric Field Influences charge q - - - E-field units are   [N/C] - - - - - - - -
When any electric charge q is immersed in an Electric Field,
      => F_{on q} = q E . . . (similar to gravity's F_{on m} = m g
. . . this influenced charge {lower case} does NOT contribute to the E-field at its own location
      (charges cannot push on themselves ... we cannot divide by zero distance)

Electric conduction - - - - - - - - - - - - - -
Electric Force tends to cause acceleration of the object which carries q .

. . . conductive material allows charge (electrons) to move thru its bulk (metal)
      placed in a → E-field , its (−) electrons travel ← thru the metal , leaving (+) ion cores on the right side;
      . . . they accumulate until (pico-seconds later) their (−)←(+) E-field contribution cancels the original field.
      => e⁻ re-arrangement reduces the interior E-field to zero

. . . insulative material does not ... each electron is held tightly to one molecule (glass)
      dielectric material allows each e⁻ cloud to displace slightly (into E-field) from its positive ion core
      => induced polarization reduces the interior E-field by factor κ (< 7 , usually), so Q can be κ× larger for same E .