Constants: Electric Potential (static case!) - University of Alabama

Constants:

ke 1/4 o = 8.98755 ? 109 N ? m2 ? C-2 o = 8.85 ? 10-12 C2/N ? m2

?o 4 ? 10-7 T ? m/A c2 = 1/?o o

e = 1.60218 ? 10-19 C me- = 9.10938 ? 10-31 kg mp+ = 1.67262 ? 10-27 kg

NA = 6.022 ? 1023 things/mol g = 9.81 m/s2

Basic Equations:

0 = ax2 + bx2 + c = x = -b ? b2 - 4ac

2a

mv2

Fcentr

=

- ^r Centripetal r

Electric Force & Field:

F12

=

ke

q1 q2 r2

^r

=

q2 E1

E1 E

= =

F12 /q2

=

ke

q1 r2

ke

X

i

qi ri2

^ri

^r ke

?

dq

?

r2 ^r = ke

^r r2 dVol

Capacitors:

Qcapacitor = CV

Cparallel plate =

0A d

Ucapacitor

=

1 QV

=

Q2

= C (V )2

2

2C

Ceq, par = C1 + C2 + C3 + ? ? ?

1/Ceq, series = 1/C1 + 1/C2 + 1/C3 + ? ? ?

Cwith dielectric = Cwithout

air = 1

I = dQ/dt = CdV /dt

RC circuits

QC (t)

=

Q0

h 1

-

e-t/

i

charging

QC (t) = Q0e-t/ discharging

Q(t) = CV (t)

= RC

ac Circuits

= L/R RL circuit

= RC RC circuit

1

XC

=

"resistance" of a capacitor for ac 2f C

XL = 2f L "resistance" of an inductor for ac

1

cutoff

=

= 2f

Electric Potential (static case!):

U

?B

V = VB - VA =

q

= - E ? dl

A

q Vpoint = ke r?

dq V = ke r

continuous

dV Ex = - dx E = -V

Upair of point charges

=

ke

q1 q2 r12

= V1q2 = V2q1

Usystem

=

sum

over

unique

pairs

=

X

pairs ij

ke qi qj rij

1? Ufield = 2 ?

oE2 dVol

=

1 2

?

dq

V dVol

V = ke

continuous r

dV Ex = - dx E = -V

P E = qV = -q|E||x| cos = -qExx

constant E field

Other:

"

"

E2 - E1 ? n^ = 4ke sheet of charge with

Fsheet = 2 (E1 + E2)

Current & Resistance:

?

I=

S

J ? dA

uniform J

-----

I

=

dQ dt

=

nqAvd

J

=

X nk qk vk

-u-n-ifo-rm-J

J

=

I A

=

nqvd

?

k?

d

J ? dA = -

S

dt

dVol

V

l R = = 1/

A

q

vd =

E m

= scattering time

m = 1/ =

nq2

R = V /I Ohm

E = J orJ = E Ohm

P = dU/dt = IV power

Req = R1 + R2 + . . . series

1/Req = 1/R1 + 1/R2 + . . . parallel XX

Iin = Iout junction

X V = 0 loop

closed path

EM Waves:

|E| c = f =

|B|

? photons ? ? energy ? ? 1 ? I=

time photon Area

I=

energy = EmaxBmax = power (P) = Em2ax

time ? area

2?0

area

2?0 c

1

Magnetism:

FB = qv ? B

dFB = Idl ? B I-carrying wire

dB = ?o Idl ? ^r wire 4 r2

B = ?0I ^ loop 2r

B=

?oN I l

= ?onI

solenoid

FB = ?oI1I2 2 wires l 2d

B = B ? dA

= ? ? B with ? = IA I loop

U = -? ? B dipole

Ufield =

1? 2?o

B2 dVol

Induction & Maxwell

V = |v||B|l = |E|l motional voltage

L = N B /I

VL = -LdI/dt

L = ?oN 2A/l solenoid

I

=

" (V /R) 1

-

e-t/ "

= L/R

LR close

I = (V /R) e-t/ = L/R LR open

U = 1 LI2 2

M12 = N212/I1 = M21 = N121/I2 = M

V2 = -M dI1/dt - LdI2/dt

V = E ? dl = - dB dt

V = Blv motional

E =

E ? dA = 4keqencl =

qencl

o

B ? dA = 0

B

?

dl

=

?o I

+

1 c2

dE dt

mutual

Optics:

hc E = hf =

speed of light in vacuum c

n=

=

speed of light in a medium v

1 = v1 = c/n1 = n2 refraction

2

v2 c/n2 n1

n1 sin 1 = n2 sin 2 Snell's refraction

f = c

h

q

M=

=-

h

p

1

11 2

=

+=

mirror & lens

f

pq R

n1 + n2 = n2 - n1 spherical refracting

pq

R

q = - n2 p flat refracting n1

1 = ,, n2 - n1 ? ? 1 - 1 ? lensmaker's

f

n1

R1 R2

Vectors:

q |F| = Fx2 + Fy2 magnitude

= tan-1 ? Fy ? direction Fx

^r = r/|r|

dl = dx x^ + dy y^ + dz ^z

let a = ax x^ + ay y^ + az ^z and b = bx x^ + by y^ + bz ^z

n

X a ? b =axbx + ay by + az bz = aibi = |a||b| cos

i=1

|a ? b| = |a||b| sin

x^ y^ ^z

a ? b = ax

ay

az

=

(ay bz

-

az by )

x^

+

(az bx

-

axbz )

y^

+

(ax by

-

ay bx)

^z

bx

by

bz

Derived unit

newton joule watt coulomb V farad ohm tesla electron volt -

Symbol

N J W C W/A = m2?kg/?s3?A F T eV 1 T ? m/A 1 T ? m2 1 N/C

equivalent to

kg?m/s2 kg?m2/s2 = N?m

J/s=m2 ?kg/s3 A?s

C/V = A2?s4/m2?kg V/A = m2?kg/s3?A2 Wb/m2 = kg/s2?A

1.6 ? 10-19 J 1 N/A2 1V?s 1 V/m

Power Prefix Abbreviation

10-12 pico

p

10-9

nano

n

10-6

micro

?

10-3

milli

m

10-2

centi

c

103

kilo

k

106

mega

M

109

giga

G

1012

tera

T

Right-hand rule #1

1. Point the fingers of your right hand along the direction of v. 2. Point your thumb in the direction of B. 3. The magnetic force on a + charge points out from the back of your hand.

Right-hand rule #2: Point your right thumb along the wire in the direction of the current. Your fingers curl around the direction of the magnetic field, which circulates around the wire.

2

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