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Physics 2 UF formula sheet, Cheat Sheet of Physics

Formula sheet include electric forces, fields and gauss laws, electric potential and capacitors, electric current and circuits, magnetic fields, interferences and diffractions.

Typology: Cheat Sheet

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PHY2049 Formulas: Sheet 1
Chapter 21 – 23 (Electric forces and fields, Gauss’ law)
Coulomb’s Law 22
0
ˆˆ
4
kQq Qq
rr
πε
=≡Fr r
(point charge) ˆ
r = unit vector from Q to q.
Electric field q=FE (general) 22
0
ˆˆ
4
kQ Q
rr
πε
=≡Er r
(single point charge Q)
22
ˆˆ
or
ii
ii
kq kdq
rr
==
ErEr
(point charges or continuous)
Electric dipole cosUpE
θ
=− =−pE sinpE
τ
τθ
=
×=pE
G
Gauss’ law encl
0
Eii
iS
Q
d
ε
Φ= = =
EA EA
v "electric flux"
E
Φ
=
Chapter 24 – 25 (Electric potential, capacitors)
Work 22
11
22
f
f
ifi
i
W d K K mv mv=⋅==
Fs
Conservative force f
iiiff
i
UU d UKUK−= →+= +
Fs (energy conservation)
Electric potential
0
(general) (point charge )
4
UkQQ
VV Q
qrr
πε
==
Potential difference
(
)
f
ifi
VV VΔ≡ = Ex x (E constant) f
fi i
VV d
=−
Es (E variable)
E field from V xyz
VVV
EEE
x
yz
∂∂∂
=− =− =−
∂∂∂
Capacitors 0
A
Cd
ε
= (flat plates)
()
0
2
ln /
L
Cba
π
κε
= (cyl shell) 0
4ab
Cba
πκε
= (sph shell)
Capacitors (cont) eq 1 2 eq 1 2
111
(parallel) (series)
E
qCV E C CC C C CCC
κ
κ
=→ =+ =+
Energy 2
22
11
0
22
(energy) (energy density)
2
EE
q
UCV u E
C
ε
== =
Chapter 26 – 27 (Electric current, circuits)
Current (basic def) (using current density)
S
dq
iiJAid
dt
≡==
JA
Current density 1(using conductivity or resistivity )
ρ
σ
σρ
==JEE
Drift velocity 2
/ (resistivity)
ed e e
Jenv men
ρτ
==
pf3
pf4
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PHY2049 Formulas: Sheet 1

Chapter 21 – 23 (Electric forces and fields, Gauss’ law)

Coulomb’s Law 2 2 0

kQq Qq

r πε r

F = rr (point charge) r ˆ = unit vector from Q to q.

Electric field F = q E (general) 2 2 0

kQ Q

r πε r

E = rr (single point charge Q )

2 2

ˆ (^) or ˆ i i i (^) i

kq kdq

r r

= (^) ∑ = ∫ E r E r (point charges or continuous)

Electric dipole U = − p E ⋅ = − pE cos θ τ= p × E τ= pE sinθ

G

Gauss’ law

encl

0

E (^) i i i S

Q

d

Φ = (^) ∑ ⋅ = ⋅ = ∫

E A E A

v Φ (^) E ="electric flux"

Chapter 24 – 25 (Electric potential, capacitors)

Work 1 2 1 2 2 2

f f i f i i

W = ⋅ d = KK = mvmvF s

Conservative force

f f i i i f f i

UU = − ⋅ dU + K = U + KF s (energy conservation)

Electric potential

0

(general) (point charge ) 4

U kQ Q V V Q

q r πε r

Potential difference Δ V ≡ V f − V i = − E ⋅ ( x f − x i )( E constant)

f f i i

VV = − ⋅ dE s ( E variable)

E field from V (^) x y z

V V V
E E E

x y z

Capacitors

0 A
C

d

= (flat plates) ( )

ln /

L
C

b a

= (cyl shell) (^4 )

ab C b a

(sph shell)

Capacitors (cont) (^) eq 1 2

eq 1 2

(parallel) (series)

E

q CV E C C C C C C C C

Energy

2 1 2 1 2 2 (energy)^20 (energy density) 2

E E

q U CV u E C

Chapter 26 – 27 (Electric current, circuits)

Current (basic def) (using current density) S

dq i i JA i d dt

J A

Current density 1 (using conductivity or resistivity ) ρ

J = σ E = E σ ρ

Drift velocity

2 / (resistivity) e d e e

J = en v ρ= m e n τ

Resistance eq 1 2 eq 1 2

(series) (parallel)

L

V iR R R R R A R R R

Temp dependence ( )

0 0 0

ρ − ρ = ρ α T − T

RC circuits ( )

/ / max max 1 RC^ (charging) RC (discharging)

t t RC RC q q e q q e

τ τ

− − = = − =

Circuits (1) Current entering junction = current leaving junction (2) 0 (over loop) i i

∑ V^ =

Power in circuit

2 P = iV (general power eqn) P = i R (power lost in resistor)

Chapter 28 – 29 (Magnetic fields)

Magnetic force F = q v × B F = qvB sin φ (charge) F = i L × B F = iLB sin φ (current)

Magnetic dipole μ = NiA (current loop)

τ = μ × B τ = μ B sin θ (torque) U = −μ ⋅ B = −μ B cos θ (potential energy)

G G G

Generating B field 0 0 2 2

ˆ (^) sin (Biot-Savart law) 4 4

id ids d dB r r

×

s r B

0 0 enc (Ampere's law)^ (long wire) 2

i d i B r

B s

v

0 0 (circular loop) (partial loop) 0 (solenoid) 2 4

i i B B B ni R R

Force between currents 0

2

a b ab

i i L F d

B field of dipole ( )

0 3 2

z z

B =
G

(very far from dipole)

Thermal energy 3 2 B

K = k T per molecule

EM waves sin (^) ( ) sin (^) ( ) 2 / 2 / m m E = E kx − ω t B = B kx − ω t k = π λ ω = π f c = λ fk

1 1 0 0 max rms 2 2

E = Bc c = 1/ μ ε Em = E B = Bm

Intensity and power

2 2 ave rms rms 0 0 0

1 1 c I S E B

μ c μ μ

S = E × B = = =

2

(abs), (refl) 4

r

P I I

I p π r c^ c

Polarization

(^2 )

I = I 0 cos θ I = 2 I unpolarized

Refraction 2 2 1 1 2 2 1 1

sin sin sin (^) c tan B

n n n n n n

Chapter 34 (Images)

Lens equations (^) ( ) 1 2 1 2

(mirror) 1 (lensmaker's eqn)

i m f R n p i f p f r r

Magnifier

25cm 25cm m (image at ), 1 (maximum) f f

θ

Telescope, microscope

obj

eye obj eye

(telescope) (microscope)

f m M f f f

θ

Spherical lens

n 1 (^) n 2 (^) n 2 (^) n 1

p i r

Chapter 35 – 36 (Interference and diffraction)

Interference / 2 / path length n n

λ = λ n Δφ = π Δ L λ Δ L =

Thin film ( )

1 1

1

2 d = m λ n (constructive) = m + 2 λ n (destructive) ( n 0 < n 1 < n 2 )

Diffraction d sin θ = m λ(max, 2 slit or grating) a sin θ = m λ(min, single slit)

Δ θ = 1.22 λ/ D (Rayleigh criterion) Δθ ≈λ/ d (interferometer resolution)

Intensity diffraction

2 2 sin sin 2 sin sin m (1 slit)^ m cos^ (2 slit)

a d I I I I

Diffraction grating

2 2 sin sin ( slits) (half-width of maxima) sin cos

m hw

N
I I N

N Nd

⎛ ⎞ ⎛^ ⎞

avg (dispersion) (resolving power) cos

m D R Nm d

θ^ λ