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Physics 2063 Exam 2 Fall 2007 Equations
Kirchhoff's Rules:
Loop Rule:  emf’s =  VD (any loop) = 0, Junction Rule: Iin =  Iout (any junction)
RC CIRCUITS:
charging: I = (emf/R)e-t/RC: Q = (C * emf)(1-e-t/RC): Vcap = (emf)e-t/RC
discharge: I = (Vmax/R)e-t/RC: Q =(Qmax)e-t/RC: Vcap = (Vmax)e-t/RC
o = 8.85 x 10 -12 C2/N M2
1. MAGNETIC FIELD EFFECTS
a) Magnetic Field Intensity: B (tesla)
b) Magnetic Force on Charge: F = q(v x B) = qvB sin  (right hand rule)
c) Magnetic Force on Current: F = I(L x B) = ILB sin (right hand rule) dF = I(dl x B)=
IdlBsin d) Magnetic Torque on Loop: = I(A x B) = IAB sin  (right hand rule)
.
Magnetic Moment: = IA , torque  =  x B = B sin Magnetic Energy U = - B = Bcos  e) Motion of a charged particle in magnetic field perpendicular to velocity:
Magnetic Force = Centripetal Force: qvB sin 90 = mv2/r ; (qvB sin  = mv2/r) general
f) e/m experiment, mass spectrometer (velocity selector: qvB = qE ==> v = E/B)
2. MAGNETIC FIELDS:
a) Biot-Savart Law: dB = (o/4) I (dl x r)/r2
b) Long straight current carrying wire: B = oI/(2  r)
c) Circular loop of wire, at center: B = oI/(2 r)
d) Solenoid, inside of solenoid: B = onI ; Toroid, inside: B = oNI /(2 r)
e) Force between two long straight conductors: F=(oI1I2)L/(2  r)
.
f) Ampere’s Law:
B dl = o Ienclosed
g) Gauss’s Law for Magnetism:
.
B dA = 0
3. ELECTROMAGNETIC INDUCTION:
.
a) Faraday's Law: EMF = - N(d)/dt where  =  B dA ;  =  B A cos 
b) L = (N the magnetic flux.
c) Motion EMF: emf = B vd
.
.
d) Faraday’s Law (2nd form):
E dl = - d/dt  B dA
e) Self Inductance: EMF = -L dI/dt (L=self inductance in Henries); L = L (long
solenoid)
f) Energy stored in magnetic field: (energy/volume) = B2/ (2o): U = LI2/2 (inductor)
4. RL Circuits with an emf source ε , with switch closed, I (t) = ε /R (1-e-tR /L) Current in
the circuit I at any time t. where R is the resistance and L is the inductance.
If the battery is removed from the circuit : I = ε /R (e-tR /L)
5.LRC Circuit (AC circuit)
I = I sin (ωt – φ) ,
ε = ε max sin (ωt )
AC circuit with capacitor: Vc = I Xc, Xc = 1/ ω C;
AC circuit with Inductor: VL = I XL
,
X L = ω L;
LRC circuit: Impedance: Z = √ ( R 2 + (XL –XC ) 2 ; I = Emf / Z
Phase angle : tan φ = (XL –XC )/ R for LRC circuit.
Displacement current Id = o (d)/dt , where,  =  E A cos where is
the electric flux.
6. Maxwell’s Equations:
E . dA = Q(enclosed)/o
.
B dA = 0
.
.
E dl = - d/dt  B dA
.
B dl = o Ienclosed + oo (d)/dt
Additional Information: Resistors in series and parallel:
Req = R1 + R2 + R3 + (series) , 1/Req = 1/R1 + 1/R2 + 1/R3 + (parallel)
Ohm’s law : V = I R
o = 4  x 10 -7 N/A2
o = 8.85 x 10 -12 C2/N M2