E&M Flashcards
Columb’s law
Fe = ke*|q1|*|q2|/r2
ke = columb constant
Columb’s constant
ke = 1/(4*π*ϵ0)
Force of Electrical feild
Fe=qE
force that acts on a point charge
direction of electrical field lines
positive charge to negative charge
acceleration of particle in uniform electrical field
a = qE/m
Electric Flux
ΦE = EAcos(θ)
θ = angle between direction electrical field and normal of area
Gaussian surface
closed surface containing charge
Net flux through gaussian surface
ΦE = E∮dA = q/ϵ0
potential energy of electric feild
ΔU = -q0 ∫ Eds
Electric potential
V = U/q0
ΔV = ΔU/q0 = - ∫ E·ds
Work done on charge in electric field
W = qΔV
Electric potential in uniform electric field
*how does electric field increase/decrease?*
ΔV = -Ed
electric field lines point in direction of decreasing electric potential
electric potential from point charge
V = ke*q/r
relationship between equipotential surfaces and electric field lines
equipotential surfaces must be perpendicular to electric field lines
electric potential due to continuous charge distribution
V = ke ∫dq/r
electric potential at surface of charged coductor
every point on surface of charged cuductor is at the same electric potential
Electric field within charged conductor
electric field inside cavity must be 0
Capacitence definition
C = Q/ΔV
Capicitence of a charged sphere
Q/ΔV = Q/(keQ/R) = R/ke = 4πϵ0R
Capicitance of parallel-plate capacitor
C = ϵ0A/d
Capacitors in parallel
Ctot = C1 + C2 + C3 …
Capacitors in series
1/Ctot = 1/C1 + 1/C2 + 1/C3 ….
Energy stored in capacitor
U = Q2/2C = 1/2*QΔV = 1/2*C(ΔV)2
Energy density
uE = U/Ad
Capacitance with dielectric
C = ϰC0
Voltage with dielectric
V = ϰV0
note: if voltage source is not turned off when dielectric is inserted, voltage will remain the same
Definition of current
I = ΔQ/Δt
Current density
J = I/A = nqvd
J = σE
σ -> is the coductivity of the conductor. (Ohm’s law)
Definition of resistance
R = ΔV/I
resistivity
ρ = 1/σ
R = ρ*l/A
temperature coeffecient of resistivity
α = (1/ρ0)*(Δρ/ΔT)
resistance at temperature
R = R0[1+α(T - T0)]
Power in resister
P = IΔV
P = I2R
P = (ΔV)2/R
Voltage in battery
ΔV = ε - Ir
ε -> emf (max possible voltage battery can provide between terminals)
r -> internal resistance of battery
Resistors in series
Rtot = R1 + R2 + R3 …
Resistors in Parallel
1/Rtot = 1/R1 + 1/R2 + 1/R3 …
Kirchof’s rules
1) Junction rule: sum of currents entering any junction in a circuit must equal the sume of the curents leaving that junction
2) Loop rule: The sum of potential differences across all elements around any closed loop circuit must be 0
RC circuit, using loop
ε - q/C - IR = 0
ε -> voltage on battery
Initial current of RC circuit
I0 = ε/R
maximum charge on capacitor in RC circuit
Q = Cε
charge as a function of time in charging RC circuit
q(t) = Cε(1 - e-[t/RC]) = Q(1 - e-[t/RC])
current as a function of time in charging RC circuit
I(t) = (ε/R)e-t/RC
charge as a function of time for discharging capacitor in RC circuit
q(t) = Qe-t/RC
current as a function of time for discharging RC circuit
I(t) = -(Q/RC)e-t/RC
Galvanometer
- measures current and voltage
- uses torque of magnetic field generated from coil
- connect in series to measure voltage
- connect in parallel to measure current
Ammeter
- measures current
- should ideally have 0 resistance
- connect in series
Voltmeter
- measures voltage
- ideally has infinite resistance
- connect in parallel
direction of magnetic field lines
north to south
force on charged particle in magnetic field
FB = qv x B = |q|vBsinθ
θ -> angle between v and B
Magnetic force on current carrying wire
FB = ILxB
symbol for magnetic feild out of page
•
symbol for magnetic field into page
x
Right hand rule
magnetic force from closed current carrying loop in magnetic field
FB = 0
magnetic force on curved current carrying wire
equal to a straight wire connected to end points carrying the same current
maximum torque on current carrying loop in magnetic field
τmax = IAB
torque of current carrying wire in magnetic field
τ = IAxB = IABsinθ
θ -> angle of magnetic field B and normal of area
radius of motion of charged particle in magnetic field
r = mv/qB
velocity selector for electric and magnetic field
qE = qvB
v = E/B
Biot-Savart law
dB = [μ0/4π][I*ds x r/r2]
magnetic field from current in infinite long wire
B = μ0I/2πr
magnetic force between 2 parallel wires
Fb/L = μ0I1I2/2πa
Ampere’s law
∮B•ds = μ0I
magnetic field inside radius of conductor
B = (μ0I/2πR2)r
(linear)
magnetic field of solenoid
B = μ0(N/L)I = μ0nI
- N -> numer of turns*
- L -> length*
- n -> N/L*
Magnetic flux
ΦB = BAcosθ
Gauss’s law for magnetism
∮BdA = 0
magnetic flux through a closed surface is always 0
Faraday’s law of induction
V = -dΦB/dt
direction of current from enduced emf (lenz’s law)
magnetic field from current must oppose the change of magnetic field from the magnet
emf for AC generator
ε = NABωsin(ωt)
Maxwell’s equations
∮EdA = q/ε0
∮BdA = 0
∮Eds = -dΦB/dt
∮Bds = μ0I +μ0ε0dΦE/dt
self induced emf in inductor
εL = -LdI/dt
Kirchof Loop for RL circuit
ε - IR - LdI/dt = 0
current in RL circuit
I = ε/R(1 - e-[Rt/L])
Energy stored in inductor
U = (1/2)LI2
Total energy stored in LC circuit
U = UC + UL = Q2/2C + (1/2)LI2
charge as function of time for LC circuit
Q = Qmaxcos(ωt + φ)
Current as a function of time for LC circuit
I = ωQmaxsin(ωt + φ)
Electric field from continuous charge distribution
E = ke*Int(dq/r2)
