~
12
= kq
1 q
2
( r
12
)
2
ˆ
12
=
= k
Z dQ r
2
~a =
E = m
V q

~
D

= qd
——————
Charge densities
——————
Q = ρV
Q = σA
Q = λ`
1.
Charges, Forces, & Fields
E
~a k
~
D d
~ ij q i
Q r ij
ˆ ij
: Force from i on j ,
: Charge of particle
N i , C
: Charge of source particle, C
: Distance from i to j , m
: Unit vector in direction from
: Electric field, N C
−
1
: Energy, J
: Acceleration, ms
−
2
: Coulomb’s constant i to j
: Dipole moment
: Distance separating charges on dipole
2.
Electric flux and Potential
 The net flux through any closed surface surrounding a point charge independent of the shape of the surface.
q is given by
 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 q in
/ o and is
∆ V
Φ
Φ
E
E
AB
= q encl
I
ε o
=
G.S.
= kq
∆ E p
=
=
Z
−
A q ∆ V
B
·
1 r
A
−
1 r
B
· d ~ d~
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
C
−
1
: Change in voltage from A to B
: Permittivity constant of free space
: Potential energy, J
——————
Electric fields
—————— rod of infinite length : 2 kλ/r sheet of infinite surface : σ/ 2 o
3.
Capacitance working voltage dielectric
: Maximum safe capacitor potential difference before dielectric breakdown
: A nonconducting material whose presence between capacitor plates increases capacitance
V
E p
Q
Qd
= Ed =
=
1
2
CV
2
= CV
ε o
A
(for PPC)
(for PPC)
E
C p
E
E p
=
=
=
κ
ε o
A d
1
2
ε o
E
2
ε o
Z
E
2 dV
2
(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 d
A
E p
C
κ
E p
E
τ
: Voltage, V
: Distance between plates of PPC,
: Surface area of one plate of PPC, m m
2
: Potential energy, J
: Capacitance, F =
: Dielectric constant
CV
−
1
: Electric energy density, J m
−
3
: Electric dipole moment for two charges of equal and opposite magnitude separated by distance ` in direction from + to
−
: 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.
I dQ
=
= dt nqvA
V = IR
R
J
ρ
P
ρ`
=
A
I
=
A
1
=
=
σ
IV
=
τ = RC
I n
J
τ
`
A
P
R
ρ
σ
: Current, A
: Number of charge carriers with charge velocity v passing through area A q
: Resistance, Ω
: Resistivity
: Conductivity
: Length of resistor,
: Surface area, m
2 m
: Current density
: Time constant
: Power, W and
5.
Magnetism ferromagnet paramagnet diamagnet
: Metal whose atoms’ magnetic moments are all aligned in same direction
: Substance with atoms having permanent magnetic dipole moments
: Substance whose atoms’ dipole moments are in reverse direction of field
I
τ
~
B
=
×
= + q~
× mv
2 r =
× qB f c
=
2 πm
= I~ ×
V
H
IB
= nqt
= H c
IB t
=
µ o
4 π
I Z
×
~ r
2
= max
=
=
×
·
E p
=
−
~
· v s
= E/B
F w
=
µ
0
I
1
I
2
`
2 πd
· d~ = µ o
I r f
~
N c
V
H n
H c
µ o
τ v s
F w s t
: Magnetic field, T
: Radius of path in magnetic field
: Cyclotron frequency
: Conductor length current direction vector
: Hall potential
: Number of charges per unit volume
: Hall coefficient
: Permeability of free space
: Torque in a currentcarrying loop
: Magnetic dipole moment
: Velocity selector velocity
: Force on wire carrying carrying I
2 distance d
I
1 parallel to wire apart
: Solenoid magnetic field
: Toroid magnetic field
: Number of turns in coil
——————
I
I
S
·
Maxwell’s equations
· d ~ = d ~
ε o
= 0 q
—————— s
~ t
=
=
µ o
N I
L
µ o
N I
2 πr
S
I
I
· d~ =
− 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
Φ
B
E
: Inductance, V sA
−
1
: Magnetic flux density, T
: Induced emf, V
= kgs
−
2
A
−
1
L =
N Φ
B
I
V
L =
Φ
B
= dI/dt
Z
· d ~
E
E
I p
=
=
=
− d Φ
B dt d Φ
E
ε o
1
2
LI dt
2