Physics 1402
Formula Sheet
Chapter 19: Electric Charges, Forces, and Fields
q1 q2

F k

F  qE


r
2
q

Ek

  EA cos 
r2
Qencl
0
Chapter 20: Electric Potential and Electric Potential Energy
U
q0

V 

Ex  

q
r
qq
U k 1 2
r

V
V
V
, Ey  
, Ez  
x
y
z
V k

Q  CV

C   0

U

A
(parallel-plate capacitor)
d
1
Q2 1
CV 2 
 QV
2
2C 2
1
uE   0 E 2 (energy density)
2
Chapter 21: Electric Current and Direct-Current Circuits

I av 
Q
t

I  lim
Q
t  0 t

Pav 
U
t

P  IV

V  IR

P  I 2R 

R
V2
(for resistor)
R
L
A
Resistors and Capacitors in Series and Parallel
1
1
1
 Series:



Req  R1  R2   RN
Ceq C1 C2

Series:

Parallel:
1
1
1



Req R1 R2

1
RN

Parallel:
Ceq  C1  C2 
RC Circuits
Charging:

t


q (t )  C  1  e RC



  
I  t     e RC
R
t




Discharging:

t
RC

q(t )  Q0 e

Q 
I  t   0 e RC
RC
t

1
CN
 CN
Physics 1402
Formula Sheet
Page 2
Chapter 22: Magnetism

F  q vB sin 

r

B

F  ILB sin 
E
(velocity selector)
B

v
mv
(uniform magnetic field)
qB

B
0 I
(long, straight wire)
2 r

B  0 nI (inside ideal solenoid)

F
 0 I
0 I1 I 2 L
2 d
Chapter 23: Magnetic Flux and Faraday’s Law of Induction

  BA cos 

 av
 N

t
Motional EMF



I
B v

B v
R

B 2 2v
R
B2v2 2
P
R
F
Inductance
 av

I
L
t


1
U  LI 2
2

Vp

 N2 
L  0 n 2 A  0 
A


(solenoid)
B2
uB 
(energy density)
2 0
Transformers
Vs

Np
Ns

Is N p

I p Ns
Physics 1402
Formula Sheet
Page 3
Chapter 24: AC Circuits
Root-mean-square Voltages and Currents
I max
V
 Vrms  max

2
2

I rms

2
Pav  I rms
R

2
Vrms
(average power dissipated in resistor)
R
Capacitors in AC Circuits
1
1
XC 

 Vmax  I max X C
C 2 fC

Vrms  I rms X C

Z  R X

Vrms  I rms Z

  tan 1 

X L   L  2 fL

Vrms  I rms X L

Z  R X

Vrms  I rms Z

  tan 1 

Z  R2   X L  X C 

Vrms  I rms Z

0 
RC Circuits
2
2
C

Vmax  I max Z

Pav  I rmsVrms cos
 XC 
R
 cos 1   (phase angle by which voltage lags current)

Z
 R 
Inductors in AC Circuits
 Vmax  I max X L
RL Circuits

2
2
L
 XL
 R

Vmax  I max Z

Pav  I rmsVrms cos

1  R 
  cos  Z  (phase angle by which voltage leads current)
 

RLC Circuits and Resonance
1
LC
 X  XC
  tan 1  L
R

2

Vmax  I max Z

Pav  I rmsVrms cos

f0 
1
2 LC

1  R 
  cos  Z  (phase angle by which voltage leads current)
 

Physics 1402
Formula Sheet
Page 4
Chapter 25: Electromagnetic Waves

Propagation of Electromagnetic Waves & The Electromagnetic Spectrum
1
c
vf

 0 0
Energy in Electromagnetic Waves

1
uE   0 E 2
2


utotal  uE  uB  0 E 2
U
I av 
At
P
I
A

 1
uB  
 20
E  cB

Pav 

I  c0 E 2



 2
B

U
t
Polarization
1
I trans  I 0 (for unpolarized light hitting a polarizer)

2
Itrans  I0 cos2  (Law of Malus)
Chapter 26: Geometrical Optics


Reflection of Light & Spherical Mirrors
1
 r  i (Law of Reflection)
f  R

2
hi
d
1
1 1
 
m
  i (magnification)
(Mirror Equation)

d o di
f
ho
do
Refraction of Light
c
n

v


1
1 1
 
(Thin-lens Equation)
d o di
f
n1 sin 1  n2 sin  2 (Snell’s law)
Thin Lenses

m
hi
d
  i (magnification)
ho
do
Chapter 27
Refractive power = 1/f; f – number = f/D
Magnifying glass M = N/f; or M = 1+ N/f; Microscope: M = -(di N)/(fefo); Telescope: M = fo/fe, L = fo+fe
Chapter 28: Physical Optics

2

2


Superposition and Interference
(condition for constructive interference)
1  m , m  0, 1, 2,
1
1

  m    , m  0, 1, 2,
2

(condition for destructive interference)
Young’s Double-Slit Experiment
d sin   m , m  0, 1, 2, (constructive interference)

1

d sin    m    , m  0, 1, 2,
2


small-angle approximation:
(destructive interference)

y  L tan 
Physics 1402
Formula Sheet
Page 5
tan   sin   



For thin film, you need to consider if there
is a /2 change; also the  changes in the
medium to /n.
Diffraction
W sin   m , m  1, 2, (destructive interference – single-slit diffraction)
d sin   m , m  0, 1, 2, (constructive interference – diffraction grating)
Modern Physics
E1
13.6
  2 eV
2
n
n
 t
 t
N  N 0e , R  R0e
ln 2
T1/2 
, T1/2 ( 14C )  5730 years
rn  n 2 r1 ,

r  1.2 1015 A1/3 (m)
m0v
p
1  v2 / c2

E

1 v / c
K  E  E0
p  E/c


2
2
, E0  m0 c 2


1
1 
 1
 R 2  2 

n 
m
Wien ' s law f peak  5.88 1010 T

p

En  nhf , n  0,1, 2, 3,...

K max  hf  W0

f0 

   

t 
h
(1  cos  )
me c
L  L0 1  v2 c2
N  m2

k  9.00 109

 0  8.85 1012
C2

1 
k 

4 0 

C2

N  m2
Tm
0  4 107
A
19
e  1.60 10 C (magnitude of charge on electron)

me  9.111031 kg (mass of electron)

m p  1.673 1027 kg (mass of proton)

mn  1.675 1027 kg (mass of neutron)

1 eV  1.602 1019 J
c  3.00 108 m/s (speed of light in vacuum)
h  6.626  1034 J  s (Planck’s constant)



E  hf
Physical Constants

h



m0 c 2

En 
W0
(cutoff frequency)
h
t0
1  v2 c2
Physics 1402
Formula Sheet

Areas & Volumes


Circumference of a circle, radius r : C  2 r
Area of a circle, radius r : A   r 2

Surface area of sphere, radius r : A  4 r 2
4
Volume of sphere, radius r : V   r 3
3
Area of lateral surface of a right circular cylinder, radius r , length




Page 6
Volume of right circular cylinder, radius r , length
Trigonometric Identities

sin  A  B   sin A cos B  cos Asin B

sin(t  90 )  cos t
: V r
2
: A  2 r