ELECTRIC FIELD: E in units of Newtons/Coulomb (Volts/Meter): E = F/q   9; (defining Equation)

E = k Q / r2 (generated by a point charge) E = (2 k l )/ r (from 'infinite' line of charge)

E = s / eo (at surface of conductor) E = s / eo (between parallel plates)

E = s /2 eo (infinite sheet of charge)

ELECTRIC DIPOLE: (Equal and opposite charges separated by a distance L.)

p = q L (Dipole Moment) t = p x E (Torque on dipole) U = -p . E (Dipole Energy)

ELECTRIC POTENTIAL (work/unit charge): V = Work/Charge (Volts = Joule/Coulomb)

a) dV = - E . dx (E = - dV/dx) or Vab = - E . dx & V = -E . d = -Ed cos f (E constant)

DIELECTRICS/DIELECTIC CONSTANT: K = (electric field in vacuum/electric field in dielectric): E = Eo/K

uE = (eo E2)/2 [Joules/Meter3] (Energy density of an Electric field)

E . A = Electric Flux E . dA = Q(enclosed)/eo E . dl = 0

MAGNETIC FIELD EFFECTS

Magnetic Field Intensity: B (tesla or webers/m*m)

Magnetic Force on Charge: F = q(v x B) = qvB sin q (right hand rule)

Magnetic Force on Current: F = I(L x B) = ILB sin q (right hand rule) [dF = I(dl x B)= IdlBsin q]

Magnetic Torque on Loop: T = I(A x B) = IAB sin q (right hand rule)

Magnetic Moment: m = IA      (so T = m x B = mB sin q )

Magnetic Energy U = -m . B = -mBcos q

MAGNETIC FIELDS: Biot-Savat Law: dB = (mo/4p) I (dl x r)/r2

Long straight current carrying wire: B = moI/(2 p r)

Circular loop of wire, at center: B = moI/(2 r)

Solenoid, inside of solenoid: B = monI Toroid, inside: B = moNI /(2 p r)

Magnetic materials: let Km = relative permeability then: B (internal) = KmB(applied)

Km =.999991 (water) : = 1.000021 (aluminum) : = 5500 (iron)

Energy density of magnetic field: = B2/ (2mo)

Gauss’s Law for Magnetism: B . dA = 0 Ampere’s Law: B . dl = mo Ienclosed

ELECTROMAGNETIC INDUCTION:

Faraday's Law: EMF = - N(dF)/dt    (where   F = ò B . dA  =    F =ò B A cos q )

Lenz's Law: Induced emf opposes the change in flux

Faraday’s Law (2nd form)    9; E . dl = - d/dt [ò B . dA ]    [Motion EMF: emf = B vd]

Mutual Inductance: EMF = - M dI/dt (M=mutual inductance in henries)

Self Inductance: EMF = -L dI/dt (L=self inductance in henries); L = moN2A/L (long solenoid)

Transformers: Vp/Vs = Np/Ns & Ip/Is = Ns/Np

mo = 4 p x 10 -7 N/A2       eo = 8.85 x 10 -12 C2/N M2