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Unformatted text preview: Ca acitance Electric Field [NEG] Capacitance: (f‘ =
' . r . ASE
Capacrtance ofa Parallel Plate Capacrtor: (7‘ : (Jay : 0T 1 “'1 ‘ Point Charge: E = __
4» bn 4:? r
hub/m 1 d
’ (I!) “ Electric Dipole; E = _é‘_ Spherical Capacitor: 435D I t 233' Z
J 7 (r , Cylindrical Capacitor: ~ ' w I‘ w w w . . _ c 1 n . . Capacrtors in Parallel:(, gq : C1 +(, 2 +(, 3 Contmunug C] 8 HE E u n: E = I r = matenal radius
I ~ . a t 1 l 1 l 43.13  C apacrtors in Series: : + + _l ("W (f'1 ("2 ('3 Inside :1 Conductor: E = D
. c _
Capacitor ('1 and C2 in series_ ('12 and ('3 in parallel: 71 = (71 r CIutmde Charged Conductor: E = — where c : surface charge density = q A
12] "12 ' E C
i : ﬂ : K2 : Atlas7 Charged Rnd' E = ’1 where i = linear char density =i
T" V T" ' 23.? r ge I
i : q : K2 : Afr" E T" V/z; T" a" Unjﬁirmly Charged SheetE = 2— , E Charging (Discharging) a Capacitor: C' : # where E : emf . or C" 7 ‘ Capacitor with a Dielectric (constant V): (f' : Capacitor with a Dielectric (constant q): (f‘ : Inside Two Plates:E = 2'5 E
A Capacitive Load: 4Y0 = V e Outside Tm Plates: E = U mmem Spherical 51:11 nfCharge q and Radius R: E = CI E  L 1Where r = dist to Gaussian surface W _
4m: 3‘ n’
(‘llrel‘nti i: —q Url.i.‘li1rm13.r Charged Sphere nfCharge q and Radius R: E = same as spherical shell, E = [ijr (it 421.? R If the current due to the motion of positive charges. the current arrow parallel to the _ 5V
. . ,; DuetoPutenualV:E =—
charge relocrtx r . as If the current due to the motion of negative charges. the current arrow antiparallel
t0 the charge velocitr t. The component. of E in any direction is the negative ofthe rate at whichthe electric potential changes with Current Density: i: ll (constant J). t: (valiahle J) dimmce in this EliTecum With Emcg Due to Potential v: E = — W R
BrﬂnCh imrtmt : flstgbmnch +i1udibnmch Conductor in an External Electri: E = U E = GI—
W
E The current i through a conductor is proportional to the voltage 1" applied across it. The sum of currents entering anyjlurction is equal to the sum of currents leaving the point Charge “5th a Dialecti3; E = 1 i
junction. 43’“? r An induced current has a direction such that the magnetic ﬁeld due to the induced current W W5C]
opposes the change in the magnetic ﬂux that induces the current
CI— ‘, , I, : Br 4,! p 1 Isolated Conductor Immersedin Dielectric: E = — RL(1rcult.Jtrt: ill — e where r : 7 KB
R R E
. . E 1 mi: ; =
RL Circuit (battery removed): «'11): Ea“ where f : E A“ v“ E K
E Due to Res'EﬁIIity: E = a?
Series RCL (‘ircuitifz Jsintnr— phvhere I : j" and Z : I: ' A ’ 1 Due to 1' I mm: Fig“: E = , . d1) E . _
Displacement Current: rd : an 7 Bu 1], Flu; g E . d3 = _
I .. Emf[\'] Encrgv Dcnsitv [1/1113] Flux [N ~ In2 / C]
D A i ’ W k'E7dW : * ‘
lie to a 1. iange in or . 7 d , , 7 , ” , Electric Field (I) I (7
Ideal: E : 1"
Real: E : T’ + fr where r : the device‘s inteinal resistance of the eivandeVice
Single Loop (‘ircuitE : Rf7> E 7 ii? : 0 Gaussian Surface: 80(1) : q . 80 iii ~ d; : q Mir/marl mvr/mw/ Magnetic: (1)8 = [bldd
Changing lVIagnetic Flux through a Loop: (I) B = J. Bil—'1 cos g6 = [F 414:1 . : a .  . .. ‘ .. I Inductance of a SolenoidﬂDB = Li ' 7 “WWW mm” “mm “m "HG? .w —g—Ma netlzatlon [A/m] lVlutual Inductance (D1 = Ni; and (I): = Vii Ellu vhnnuc m 11:.» holunnul Magnetic Flux:E : 7 M : ,Um “here [um : A _ I”, 7 e": B Mannetic Dipole Moment [J/T] (if l" 2111
Self Induction: E = 7L 7
(if B . Mannetic Di ole Moment: 1 : NA 'here N = n niber of 100 s
‘ ‘ d, . Curie’s Law: M = C— where C Is aconstant ” p i I W u p
RL Circuit: E : l —+ rR T O . .
d’ _ _ Orbital Magnetic Dipole Moment: /,l : 01% l\lutual Induction: El : 7 7 . 7 » 7 where 3121 : constant depending on geonietiy.
f Alternating Current: E : Em sin or! where Em : mus Spin Magnetic Dipole Moment: [1,5 —
Series RCL Circuit: E : Em sin mt Force [N] Inductance [H] Resistance [(2] 1 ( a , m m: Solenoid: L : 1 I’ll/A .
Coulomb’s Law: F = llll :l‘ : F :6 1 1 ‘ l n Res1stance: R = _‘
4&1) l" 1" Inductive Load: XL : L50 1
Electric Field: F : EC (13h L
10 A Mutualuu : ~ In a Conductor: R = p—
Magnetic: FR = lqlvB sin (/5 where g6 = angle between 17 and B I] A
. A 7 A L \ r .
Magnetlc(vect01‘)tFB = (1V VI 3 \ ariable Res1stor: R = p— where L = length ot Wire and A = cross sectional area
. ‘ . V ‘ ‘ l. ‘ ‘ v. V. . ~ _ ‘ . i _ ' C i ‘
Magnetic F01 ce on a (.111 1 ent Cal 1 )ing “ iie. FR —1LB j‘illeli L : length ot \\ 11e. R Resistance Rule :
Vlagnetic Force on a Current Carrying “'ire (vector): FB = if: x B A A A A A A A 7 V ’ 7'R For a move through a resistance
V . . ‘ ‘ . V. a . a a —> lnoliou in (11: direction ol'thc cuiicilt. the change in the
l\on—Uniform Magnetic Force on a Current Carrying “ ire: dFB = 1dL x B Poem,“ A , r : M,
v . . t t . u D ,‘_ . R V r( ,7 r C,(rr(i ~VV~
honUniform Net Magnetic Force on a Current (,arrvmg W Ire F8 =1Jdli><B I —~ A A A A A :Al 7 l iR F01 “ “‘0‘ e ‘1“0“=h “ “5'5"”“9 1” [he (“‘eum“
' ‘ ’ opponlc to that ofthe Clll lCI]I’_ the change in the Inuliuu ‘ u 1‘) 3 \ L ‘. V J potential \I' 71R
Force Between Parallel (,ui‘i‘ents:an =£ PL tulml' nle [ ] R (it H s g ,r j. R _ R R R
27rd esis ms 111» eiies. (,q — 1+ 3 + 3 1:
Change in P0tenﬁal Energy: M: : ‘quE ' 6’3 Resistors in Parallel: +—+
418011: 47380133 47380113
I System of Point Charges [7 = V 3 CV: '
Stored in a Capacitor L = = q
9( ,' 2 2 Resistix'itx' [Qm] EIHZ
R Average Power for R: (P) 2 Dielectric: U = —pE cos 6? p = _
J 2
Average Power for C: <PC = 0
Average Power for L: <PL > = 0
RCL Circuit: P = [MR = I. E, avg 1m Magnetic Dipole lVIoment: U : — [15 cos 67 : —[1~F Variation of Resistivity with Temperature: p — p0 = pOMT — To) , Energy Stored in Magnetic Field: [78 = L; 2 I77 . . .
,0 : , where T : average time between colliSions. cos¢ ne‘r um where cos ¢ 2 power factor = max at ¢ = 0 Spin Quantization: U = i ' Spin Quantization Charge [C] Conductivity [S/ I q : idr I , , , ‘. ‘ ‘ ‘_ 7 —m‘\~ where h is a constant, 1775 =+li2 or l/2. 1mm" “ Conduct“  (Imam * 0 23' All charge resides on conductor surface. Cavity Walls: 61mm : 0 Charge after Dielectric: (1': (1 17 i Current Density [A/mz]
.\ K /. Torgue [Nm] Gauss’ Law: (5 : goéE‘dl or qmmd : 30(1) J _ 1 Vector: 1 = [7 X where p 2 electric dipole moment Gauss, Law with Dielectricg q : g @9301] A e A
> > '  enclosed 0 In :1 Conductor: J = GE 1
w/LC Damped Oscillations in an RCL circuit: (112') : (gem/2L COS(rl7'T+ 11) where (if: lVIagnetic: rm 2 [AB sin 6 LC Oscillations: girl : Q coslwr+ ¢ l where m : and ¢ : phase angle. Magnetic Dipole Moment: ? = [X 1 LC
Transformer
Voltage Drift S )ced [in . I c . . .
1 :1 Drift Speed (scalar): Vd = Where n = number or charges passmg a ceitaln pomt
47780 R I];
Group of Point Charges: V = V1 + V3 + P; Drift Speed (“a”): a = m3
1 qd cos (9 7 Point Charge: VP = Electric Dipole: V = hIagletic Field [T]
47:8 r
0 I‘Iolion of a Charged Particle in a ITndonn I‘Iaguelic Field: 2 ﬂ
Iql 3 7
q Helical Paths: B = ﬂ. or B = _m where T 2 period: Capacitance: V = j Isl!“ '9'?
C 7
A A A Cyclotron Particle lchelerator: B = ﬂ . or B 2 ‘fm
A conductor is an egmpotential surface. re 6 JVV 2 turns in secondary COil' ' ' , ,n_ V \Vire with Segment Length (15 and culrent i: dB = #01. 035 X r
' Dielectric, l — i W W A.
4 ¢ .“ I v v . L sir. r“ ~:B: "‘3
Work [J] — Wemf : sum of all potential changes 011g ﬁgh 1" 3m? A\ along the path f1 0111 befme to after. Circular Radius of A1. c Radius R: B = we _ if 95 = 3” : 8M3" = 2%!
. . V . g, _ 4711'? 2R Resnstne Load. 1 R — [RR 2
25is 3:2
2R2 +22I . Continuous Charge Distribution: V =
Where 1P: primary current, ’ 47ng r where r :radius of circular Orbit. (21 = angular Frequency: 273;” * l’Iiman Secondan 1 dc
J‘ 7] B = g . or B
r I S = secondary current,
NP = turns in primary coil, where r' 2 (list to point P. External: W = qAV uxrur'rml Circular Loop along Loop .L\'is: B : where R = dist to z axis. and r = hypotenuse. Electrical: WE = —qAV Root Mean Square: I’m E Alnpere’s Law: at? : puimmﬂ capacnor Inside a Long Straight \Vire: B = E #01 j!" where R = radius to wire surface. r = radius to amp 1001). ZNRZ 6] V Inside a Solenoid: B : yum where 11 = nunlher of turns per unit length. or Voltage: W = V . Jun M
Torold (donut—shaped): B 2
WW 2727"
or Charge: M] = [— l‘Iaglletic Dipole: BIZ I: &£ 2(v 2.1T 23
013133, Induced BIagnelic Fields: ‘5 B 025: = #0192305“ + #0 50 d
' r Iiisplacelnent Current: 6138' : petunia + #0 x'dmmd #0 Ia‘ BIagnetic Field Outside the Capacitor Plates: B = )
727 I‘Iaguetic Field Inside the Capacitor Plates: B = [fizz Jr
71' ...
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 Spring '08
 Cerne
 Physics

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