Physics 203 equations
Magnetism:
Forces: Fmagnetic  qv  B  I  B
or


FEM  q  E  v  B 


⃗ ∙ 𝑑𝑠 = 𝜇0 𝐼𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑
∫𝑙𝑜𝑜𝑝 𝐵
Magnetic fields from currents (Ampere’s Law):
A distance r from a straight wire: B 
0 I
2 r
At the center of a loop of wire of radius R:
In a cylindrical coil (or inductor): B 
B 
0 I
2 R
0 N I
length
0  4  107 T m / A
EMF from electric generators (Faraday’s Law and Lenz’ Law):
EMF  
dB
d
   BAN cos   where N is the number of loops
dt
dt
Circuits I: (without inductance):
V  IR
Resistors (Ohm’s Law):
Power:
Power  VI  I 2 R
Kirchhoff’s Rules:
1. Junctions: “  Iin   Iout ”,
Resistors in parallel:
Capacitors:
…in
 voltages  0
series: R1  R2  RTOTAL
Q  C V
Capacitors in parallel:
RC Circuits:
1
1
1


R1 R2 RTOTAL
2. Loops:
C1  C2  CTOTAL
… in series:
1
1
1


C1 C2 CTOTAL
Time constant:   RC
Discharging or charging:

 t 
 t  
A(t )  A0 exp  
or
A(t )  A0 1  exp   
 
  

were A is the charge, current, or voltage (depending on conditions).
Harmonic oscillators:
2
T
  2 f 
Angular frequency:
x   0 2 x
SHO Equation:
Solution to SHO Equation:
x  xeq.  xmax sin 0t   
or xmax cos 0t    , vmax   xmax , amax   vmax
where  0 is the natural angular frequency of the oscillator
Mass on a spring: 0 
k
m
Simple pendulum:
0 
g
Inductance:
EMF   L
dI
,
dt
and for a cylindrical inductor L 
 N2 A
length
For an LC circuit (capacitor and inductor):
q  qmax sin 0t    , I  q ,
EMFL   Lq ,
1
LC
0 
and
Damped and/or driven harmonic oscillators:
Damped springs: if Fspring   kx and F friction   bv
Without a driver (motor):
 bt 


2m 
2
 b 
sin  t    where   02  
 , vmax   xmax , etc.
 2m 
With a driver (motor with angular frequency ):
x  xmax e
vmax 
 F / m

2
  
2 2
0

b
m
2

F
 m  
k

2
 b
2
RLC series circuits: VC  C1 q, VR  RI , VL  LI , where q  I
Without a driver (AC source):
I  I max e
 Rt 


 2L 
sin  t   
2
 R 
where     
 , I max   qmax , etc.
 2L 
2
0
With a driver (AC source with angular frequency ):
Vmax
I max 
2
2
L  1C   R 

