Phys 205 final Formula sheet PDF

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Formula sheet with everything you will need for the final exam...

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Kirchoffs rules: the junction rule: The sum of all currents entering a junction must equal the sum of all currents leaving the junction. the loop rule: The algebraic sum of changes in potential around any closed-circuit path (loop) must be zero. Constants: K= 8.9876 X 10^9 = 1/(4πε0)

ε0=8.8542 X 10^-12 (C^2/N*m^2 or F/m)

Mass of electron: 9.10938356 × 10^-31 kilograms Variables: E=electric field[N/C] or [V/m]

ΦE = Electric Flux [Nm^2/C]

mass of proton: 1.6726219 × 10^-27 kilograms A=area vector (normal) [m^2] s=x*θ=arc length

Conversions: 1C =6.24 X 10^18 electrons or protons Point Charges: E= (k*q1)/r^2

Charge densities: Line charge density [C/m]: λ=Qtotal/Ltotal Qtotal/Vtotal

Types of capacitors: b=big radius)

qin=charge enclosed by surface [C] F= electric force qin = charge enclosed (C)

E=electric field(Nm^2/C^2)

1 µF = 1 X 10^6 F

F=(k*q1* q2)/r^2

Capacitance: C= Q/ΔV

e = 1.60218 X 10^-19 (C)

F=q*E Surface charge density[C/m^2]: σ = Qtotal/Atotal

Volume charge density[C/m^3]: p=

Energy stored in a capacitor: U= (1/2)*C*ΔV^2 = (1/2)*Q*ΔV = Q^2/2C Parallel plate: ε0*A/d (d=distance between plates) Sphere: C = 4π*ε0*(ab/(b-a)) (a=small radius and Cylindrical: C = (2*π* ε0*L)/ln(b/a) (a=small radius and b = large radius)

Gauss Law: ΦE= E*A = E*A*cos(θ) = qin/ε0 = In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The surface under consideration may be a closed one enclosing a volume such as a spherical surface.

Current [amperes]: I=ΔQ/Δt = dQ/dt Current Density, J [A/m^2]:

I = n*q*vd*A (n=charge density [e/m^3], Vd=drift velocity[m/s], A=cross sectional area[m^2]) J = I/A=n*q*vd

J = σ*E

Resistance, R [Ohms, Ω]: R = P*L/A Rnew = R0*[1+a(Tnew – T0)] area[m^2], a=temperature coefficient of material [ C ], T = temperature [C])

(P= resistivity of material [Ωm], L=length[m], A=cross sectional

DC Circuits

Series vs. Parallel circuits

Series Parallel I IT=I1=I2=I3=… IT=I1+I2+I3+… V VT= V1+ V2+ V3+… VT= V1=V2= V3=… R RT=R1+R2+R3… 1/RT=1/R1+1/R2+1/R3… *For Parallel circuits with only 2 resistors: RT=R1*R2/(R1+R2) *For series circuits with only 2 capacitors: CT=C1*C2/(C1+C2) Power, P [watts]: P=energy/time = F*v

V Q C

Series VT= V1+ V2+ V3+… QT=Q1=Q2=Q3=… 1/CT=1/C1+1/C2+1/C3+…

Parallel VT= V1= V2+ V3+… QT=Q1+Q2+Q3+… CT=C1+C2+C3+…

P=V*I = I^2*R = V^2/R

Work [J]: W=Force*distance=Change in KE=q*E*d = F*d/q = E*d = ΔV*q RC Circuits: Time constant: � = R*C (R=resistance, C=capacitance) Charging: Connected to a battery:

Discharging: Not connected to a battery: Dielectrics: C= k*C0

Dielectric =insulating material used to maintain physical separation of plates

C tends to increase when dielectrics are used by a factor equal to the dielectric constant “k”, of a material. Geometry: Sphere: V=4/3*π*r^3 sphere surface area: A=4*π*r^2 cylinder surface area: A=2πrh+2πr^2 Cylinder volume: V=π*r^2*h Cylinder lateral surface: AL=2*π*r*h Area of circle: A=πr^2 Circumference of circle: 2*π*r Random shit: F=ma Energy: KE=(1/2)*m*v^2

K=c+273(this is for temp) electric potential energy: U=K*q1*q2/r

Forces experienced by a moving charged particle in a magnetic field:

F= qvXB

(v=velocity, B=magnetic field, q=charge, F=force)

Always evaluate magnitude and direction separately: magnitude given by qvBsin(θ) and direction by right hand rule Force experienced by a current carrying wire in a magnetic field: product)

F= ILXB

(I=current, L=length(m), B= magnetic field, F=force)(“X”=cross

Force experienced by a current carrying loop in a magnetic field: Total force in the loop= 0 Motion of a particle in a magnetic field: motion is circular because of 3 finger rule.

Torque=T=IAXB = μ (magnetic dipole moment)XB

qB=mv/r

Sources of magnetic fields: Biot-Savard law=B= (μ0 *I)/4π ∫(dsXr)/r^2 Magnetic field due to a straight line segment: ((μ0 *I)/(4πa))*(sin(θ1)-sin(θ2)) Infinite length=B=(μ0 *I)/(4πa) ThumbI, fingersB

Direction:

Magnetic field due to a loop: B= (μ0 *I*a^2)/(2(a^2+x^2)^3/2)

B @ the center

of the circle= ((μ0 *I)/(2a))*the fraction of the circle Magnetic field outside of the circle always=0 ThumbB

Direction: fingersI,

Forces in a magnetic field: Magnitude abs(AXB)=ABsin(θ) direction: right hand rule A=fingers, B=palm, C=thumb Force between 2 parallel wires: F/L=( μ0 *I1*I2)/(2πa)

Currents in opposite directions repel/ currents in the same direction attract

Amperes law: For a toroid: B=(μ0*N*I)/(2πa)

for a solenoid: B=

Faradays law: ε=-N(dΦ/dt)=-N(d(BAcos(θ))/dt

(N=# of turns B=Magnetic field, A= Area, θ= angle between B and A)

Lenz law: ε=-BLv

μ0*n/L*I= μ0*N*I

(N=# of turns per unit length)

(v=velocity, L=distance between plates?)

Inductance: LC Circuit (No R): Continuously transfers stored energy from capacitor to inductor and back. Angular frequency of this circuit given by: ω=1/sqrt(LC) RLC Circuit: as long as the resistance is small, charge on capacitor will vary with time according to: Q=Qmaxe^(-Rt/2L)*cos(ωt)

where ω=sqrt((1/LC)-(R/(2L))^2)

When a capacitor is full, there is no more current flowing. When an inductor is full, there is no more resistance. AC Circuits: Idea behind it is that its being driven by a sinusoidal force V=V0cos(ωt+Φ) or V0sin(ωt+Φ)

ω= frequency = 2πf=2π/T

In AC circuits capacitors and inductors can behave like resistors:

Capacitor: Xc=1/(ωC) (Ohms)

Resistance or impedence of the entire circuit= Z = sqrt(R^2+( XL +Xc)^2) (Ohms) Root mean square (RMS) just means to divide by sqrt(2)  only when talking about power Resonant: ω=1/sqrt(LC)

Average Power: IRMS^2*Z=VRMS*IRMS*cos(θ)

cos(θ)= power factor

Transformers: VS=VP (NS/NP) IS=IP (NP/NS)

P=VPIP=VPIS

Inductor: XL=ωL (ohms) θ=arctan((XL-Xc)/R)

Electro-magnetic waves: rate at which energy passes through a unit area by electro magnetic radiation S=(1/ μ0)EXB Instantaneous magnitudes of E and B in an electro magnetic waves are related by c=E/B Radiation pressure=P=S/c

P=pressure

Radiation surface=P=2S/c

P=pressure

Energy density= u= (ε0*Emax^2)/2=Bmax^2/(2μ0) Savg=Emax*Bmax/(2μ0)= Emax^2/(2μ0*c)=cBmax^2/(2μ0)=P/A

(P=power)...