~
12
= kq
1 q
2
( r
12
) 2
ˆ
12
~
= E
~
= k
Z dQ r 2
~a = m
E = V q
| ~
D
| = qd
——————
Charge densities
——————
Q = ρV
Q = σA
Q = λ`
1.
Charges, Forces, & Fields
~ ij
: Force from i on j , N q i
: Charge of particle i , C
Q : Charge of source particle, C r ij
: Distance from i to j , m
ˆ ij
: Unit vector in direction from
~
: Electric field, N C
− 1 i to j
E : Energy, J
~a : Acceleration, ms
− 2 k : Coulomb’s constant
~
D
: Dipole moment d : Distance separating charges on dipole
2.
Electric flux and Potential
- The net flux through any closed surface surrounding a point charge q is given by q in
/ o independent of the shape of the surface.
- A conductor in electrostatic equilibrium has the following properties :
· Electric field is zero everywhere inside the conductor
· Any net charge on a conductor must reside on its surface
· Surface charge density is greatest where curvature is smallest and is
Φ
Φ
E
E
= q encl
I
ε o
=
G.S.
~ · A
∆ V
AB
= kq
∆ E p
Z
B
= −
A
= q ∆ V
1 r
A
−
1 r
B
~ · r
Z dq
V = k r
~
{
~
= x,y,z } kq r 2
∂V
= −
∂ { x, y, z }
Φ
E
∆ V
AB
ε o
E p
: Electric flux, N m
2
A to B
: Permittivity constant of free space
: Potential energy, J
C
− 1
: Change in voltage from
——————
Electric fields
—————— rod of infinite length : 2 kλ/r sheet of infinite surface : σ/ 2 o

3.
Capacitance working voltage : Maximum safe capacitor potential difference before dielectric breakdown dielectric : A nonconducting material whose presence between capacitor plates increases capacitance
Qd
V = Ed =
E p
=
1
2
CV
Q = CV
2
ε o
A
(for PPC)
(for PPC)
E
C = κ
ε o
A d p
E
=
1
2
ε o
E
2
E p
=
ε o
2
Z
E
2 dV
(for PPC)
V
C
= E ( I − e
− t/RC
) (when charging)
V
C
= V o e
− t/RC
(when discharging)
——————
Dipole shit
——————
~ =
τ = p ×
E p
= − ~ ·
V : Voltage, V d : Distance between plates of PPC, m
A : Surface area of one plate of PPC, m
2
E p
: Potential energy, J
C : Capacitance, F = CV
− 1
κ : Dielectric constant
E p
E
: Electric energy density, J m
− 3
~ : Electric dipole moment for two charges of equal and opposite magnitude separated by distance ` in direction from + to −
τ : Torque
4.
Electric current
Kirchoff ’s rules :
· The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction.
· The sum of the potential differences across all elements around any closed circuit loop must be zero.
dQ
I = dt
= nqvA
V = IR
ρ`
R =
A
I
J =
A
1
ρ =
σ
P = IV
= σ ~
τ = RC
I : Current, A n : Number of charge carriers with charge q and velocity v passing through area A
R : Resistance, Ω
ρ : Resistivity
σ : Conductivity
` : Length of resistor, m
A : Surface area, m
2
J : Current density
τ : Time constant
P : Power, W

5.
Magnetism ferromagnet : Metal whose atoms’ magnetic moments are all aligned in same direction paramagnet : Substance with atoms having permanent magnetic dipole moments diamagnet : Substance whose atoms’ dipole moments are in reverse direction of field
~
B
= v ×
~
= q ~ + q~ × mv
2 r = q~ × qB f c
=
2 πm
~
= ` ×
IB
V
H
= nqt
= H c
IB t
~
=
µ o
4 π
I Z d~ × r r 2
~ = A
τ max
= N I ~ ·
~ = µ ×
I
E p
= − ~ · v s
= E/B
F w
=
µ
0
I
1
I
2
`
2 πd
~ · d~ = µ o
I r
~
F w
: Magnetic field,
——————
T
: Radius of path in magnetic field f c
: Cyclotron frequency
~
: Conductor length current direction vector
V
H
: Hall potential n : Number of charges per unit volume
H c
µ o
: Hall coefficient
: Permeability of free space
τ : Torque in a current-carrying loop
~ : Magnetic dipole moment v s
: Velocity selector velocity
: Force on wire carrying carrying I
2 distance d apart s
: Solenoid magnetic field
~ t
: Toroid magnetic field
N : Number of turns in coil
I
1
Maxwell’s equations parallel to wire
——————
~ s t
=
=
µ o
N I
L
µ o
N I
2 πr
I
~ · A = q
ε o
I
S
~
· A = 0
S
I
I
~ · s = − d Φ
B dt
~ · d~ = µ o
I + ε o
µ o d Φ
E dt
6.
Induction
Lenz’s law : The direction of an induced emf or current is such that the magnetic field created by the induced current opposes the change in magnetic flux that created the current.
L : Inductance, V sA
− 1
Φ
B
: Magnetic flux density, T = kgs
− 2 A
− 1
E : Induced emf, V
Φ
L =
N Φ
B
I
V
L = dI/dt
Z
B
=
~ · A
E = − d Φ
B dt
E p
= d Φ
E
I = ε o
1
2
LI dt
2