Unit 8: Magnetism (v1)
AP Physics Memorization Material
Equations
1.

 
FB = qv × B
magnetic force on a moving charged particle (Lorentz Force)
2.
FB = qvBsin θ = qv⊥ B
magnitude of magnetic force on a moving charged particle, where θ is


the angle between v and B
3.
F=
4.
mv 2
r
2π r
v=
T
5.
 
FB = ∫ I d  × B
6.
 
FB = i L × B
7.
FB = IBsin θ
force needed to hold an object in circular motion

 µ o I d  × r µ o i ds × r̂
8. dB =
=
4π r 3
4π r 2
µI
9. B = o
2π r
 
 
10. 
∫ B ⋅ d  = µo I or ∫ B ⋅ ds = µo ienc
11. B = µ o nI
 
12. ΦB = φm = ∫ B ⋅ dA
 
13. ΦB = φm = B ⋅ A = BAcosθ
 
dφm
=
E ⋅ ds
∫
dt
dΦ m
15. E = −N
dt
14. E = −
ΦB
i
2
18. L = µ on A
17. L = N
20. τ L = L
23. U L =
24. ω =
magnetic flux through an area

magnetic flux through an area when B is uniform. θ is the angle


between B and the way A “faces”
Change in flux induces a circular electric field (Faraday’s Law). One
loop around circular electric field yields an emf.
induced emf by a change in a flux through N loops of wire
inductance based on a coil’s geometry
back-emf for an inductor
time constant for inductor
R
(

integrating B around a loop yields the current passing through the loop
(Ampere’s Law)
magnetic field created by a solenoid
definition of inductance
di
dt
E
−t τ
1− e L
R
−t τ
22. i = io e L
21. i =
magnetic field created by a long straight current carrying wire
induced emf in a conductor sweeping perpendicularly through a
magnetic field
16. E = Bv
19. E = −L
relationship between circular motion, radius and period

magnetic force on a current carrying wire, where B changes or direction
of wire changes

magnetic force on a current carrying wire, where wire is straight and B
is constant throughout wire’s length
magnitude of the magnetic force on a straight current carrying wire



with constant B , where θ is the angle between B and I .
element of magnetic field created by an element of a current-carrying
wire. Both the AP and the textbook versions. (Biot-Savart Law)
)
1 2
LI
2
1
LC
25. q = Qcos (ω t + φ )
Current rises to E/R after an emf is introduced to a L-R series circuit
Current decays to zero if the emf is removed from a L-R series circuit
energy stored in an inductor
angular frequency for an oscillating LC circuit
charge as a function of time on a capacitor in an LC circuit, with Q as the
amplitude, ω as the angular frequency, and φ as a phase change.
Symbols
A=
B=
E=
F=
i=I=
L= =
L=
µo =
n=
N=
q=
r=
r̂ =

r=
T=
τL =
v=
φm = Φ M = Φ B =
Units
area enclosed by a loop of wire
magnetic field
electro-motive force
force
current
length
inductance
permeability of free space
loop or coil density
number of loops
charge
radius of circle

unit vector in the direction of r
position vector
period
time constant
velocity of a charged particle
magnetic flux
meters2
Teslas
volts
Newtons
Amperes
meters
Henry
Tesla-meters/amp
1/meters
none
Coulombs
meters
meters
meters
seconds
seconds
meters/second
webers
m2
T
V
N
A
m
H
T m/A
m–1
C
m
m
m
s
s
m/s
Wb
Complex Units
T=
N
N ⋅s
=
A⋅m C⋅m
N=kg
m
s2
J=kg
Wb = T·m2
C
A=
s
V=
m2
s2
J Wb
=
C
s
H=
Tm 2 Wb
=
A
A
Right Hand Rules
Rule Name
1. Force on particle
2. Force on current
3. F on charges along wire
Rule Name
4. Current
5. Ampere’s Law
6. Lenz’s Law
7. Solenoid
Equation #
1
5, 6
16
Equation #
8,9
10
14, 15
11
straight fingers
(cause)
v of + particle
I (+ flow)
v (⊥ to wire)
bent fingers
(cause)
B-field
B-field
B-field
thumb
(result)
force on particle
force on wire
push on +
(+ end of voltage)
Thumb
(cause)
I (+ flow)
+ direction of I inside loop
opposite to dΦB dt
Fingers Wrap
(result)
B-field
B-field around loop
E-field or emf around loop
(result)
B-field inside solenoid
(cause)
I wrapping around solenoid