Download PHY2054 Exam 1 Formula Sheet

PHY2054 Fall 2015
PHY2054 Exam 1 Formula Sheet
Vectors
r
r
r
r
a = a x xˆ + a y yˆ + a z zˆ b = bx xˆ + by yˆ + bz zˆ Magnitudes: a = a x2 + a y2 + a z2 b = bx2 + by2 + bz2
r
r r
r r
r
Scalar Product: a ⋅ b = a xbx + a y by + a z bz = a b cos θ (θ = angle between a and b )
Electrostatic Force and Electric Field
r
qq
Electrostatic Force (vector): F = k 1 2 2 rˆ (r = distance between charge q1 and charge q2, units = N)
r
ε0 = 8.85x10-12 C2/(N·m2)
k = 1/(4πε0) = 8.99x109 N·m2/C2
r r
q
E = F / q2 = k 12 rˆ (units = N/C = V/m)
r
r r
Electric Flux (through the infinitesimal surface area dA): dΦ E = E ⋅ dA (units = Nm2/C)
r
Vector Area (directed area): A = Anˆ (where n̂ = normal to the surface)
r r Q
Gauss’ Law (net flux through closed surface S): Φ E = ∫ E ⋅ dA = enclosed (Qenclosed = charge enclosed)
Electric Field (at q2 due to q1):
ε0
S
Gauss’ Law: Net flux through closed surface S = the charge enclosed by surface S divided by ε0
Electric Potential and Potential Energy
r r
straight line path from A to B, ΔU = U B − U A = − qE ⋅ d (units = J)
Electric Potential Energy: work done against a constant field E in moving charge q a distance d along
Electric Potential: Work done per unit charge against a constant field E in moving charge q a distance d
r r
along straight line path from A to B, ΔV = ΔU / q = − E ⋅ d (units = J/C = V)
Electric Potential (distance r from a point charge q): V (r ) = k
Electric Potential Energy (N point charges): U =
N
q
q
N point charges: V (r ) = ∑ k i
r
ri
i =1
N
1
2
V is the electric potential at q due
∑ q V , where
to the other charges
i =1
i
i i
i
Stored Electric Potential Energy (N conductors with charge Qi and electric potential Vi):
U=
N
1
2
∑QV
i =1
i i
Capacitance (definition): C = Q/V or C = Q/ΔV (units = C/V = F)
Energy Density of the Electric Field:
u = 12 ε 0 E 2 (units = J/m3)
Electric Current and Circuits
Current (through directed area A): I =
r
r
dQ r r
= J ⋅ A = nqvdrift ⋅ A (units = C/s = A, n is the number of
dt
charged particles q per unit volume, vdrift is the average velocity of the charged particles).
Conducting Wire (length L, cross sectional area A): J = σE ,
Ohm’s Law: ΔV = IR ,
I = σEA = EA / ρ , ΔV = EL
R = ρL / A (Resistance R units = V/A = Ω)
Resistivity (at temperature T in oC):
ρ (T ) = ρ 0 (1 + αΔT ) , where ΔT = T − T0
Power (supplied by EMF ε): P = εI Power (dissipated in resistor R): P = I2R (units = J/s = W)
RC Circuits (charging capacitor C through resistor R with EMF ε):
Q(t ) = εC (1 − e −t / τ )
RC Circuits (discharging capacitor C with initial charge Q0 through resistor R):
Q(t ) = Q0e − t / τ
RC Circuits (time constant): τ = RC (units = Ω·F = s)
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