Electromagnetic Induction (topic 5, 10, 11) Flashcards
Coulomb’s law
Force between two charges at a distance ‘r’ apart
Coulomb’s law equation
F = k q1q2 / r^2
where
F = force (N)
k = constant
q1 = charge 1 (C)
q2 = charge 2 (C)
r = distance between charges (m)
k = 1 / 4πε0
Electric field strength
E = F / q
where
E = electric field strength (NC^-1)
F = force (N)
q = charge (C)
Current
Number of coulombs going by per second
Moving charge
I = Δq / Δt
where
I = current (A)mperes)
q = charge (C)
t = time (sec)
Drift velocity equation
I = nAvq
where
I = current (A)
n = # of electrons per unit volume (m^-3)
A = cross sectional area (m^2)
v = drift velocity of electrons (ms^-1)
q = charge (C)
Potential difference
To move a charge around, you need to do work. The potential difference is the work done per charge
**use p.d. instead of voltage
Potential difference equation
V = W / q
where
V = potential difference (V)
W = work done (J)
q = charge (C)
Resistance equation
R = V / I
where
R = resistance (Ω)
V = potential difference (V)
I = current (A)
Resistivity
ρ = RA / L
where
ρ = resistivity
R = resistance (Ω)
A = cross sectional area (m^2)
L = length of wire (m)
Power
Power dissipated = energy lost in heating up
P = V I = I^2 R = V^2 / R
where
P = power (W or Jsec^-1)
V = potential difference (V)
I = current (A)
R = resistance (Ω)
Trick:
Power = work / time = energy / time
Internal resistance
Batteries have their own internal resistance that eats away at some of the volts
**emf is not a force. It is a p.d. measured in volts
Internal resistance equation
ε = I (R + r) or ε = IR + Ir
where
ε = electromotive force (V)
I = current (A)
R = resistance (Ω)
r = internal resistance of the battery (Ω)
IR = what you get (V)
ε = what the battery tries to give you (V)
Ir = lost by internal resistance of the battery (V)
Magnetic field
Where the north on a compass would point
Moving charge in a magnetic field
F = qvB sinθ
where
F = force (N)
q = charge (C)
v = speed (ms^-1)
B = magnetic field strength (T)esla)
θ = angle between B and v (°)
**if sin 90° (perpendicular), then = 1
Wire in a magnetic field
F = BIL sinθ
where
F = force (N)
B = magnetic field strength (T)esla)
I = current in a wire (A)
L = length of the wire (m)
θ = angle between B and I (°)
**if sin 90° (perpendicular), then = 1
Wire with a current (hand rules for magnetic fields)
Use RHS rule (thumbs up)
thumb = current = I (A)
fingers = magnetic field B (T)
Solenoid (coil of wire) (hand rules for magnetic fields)
Use RHS rule (thumbs up)
fingers = current = I (A)
thumb = magnetic field B (T)
Moving charge (or wire (current)) in a magnetic field (hand rules for magnetic fields)
Use LHS rule for negative charges (flat palm)
fingers = magnetic field B (T)
palm = force
thumb = velocity of particles (or the current)
Use RHS rule for positive charges or current (flat palm)
fingers = magnetic field B (T)
palm = force
thumb = velocity of particles (or the current)
Gravitational and electrical potential equations
Respectively:
Vg (J kg^-1) = -GM / r
Ve (V or J C^-1) = kQ / r
Gravitational and electrical field strength equations
Respetively:
g (N kg^-1) = -ΔVg / Δr
E (N C^-1) = -ΔVe / Δr
Gravitational and electrical potential energy equations
Respectively:
Ep (J) = mVg = -GMm / r
Ep (J) = qVe = kQq / r
Gravitational and electrical force equations
Respectively:
Fg (N) = GMm / r^2
Fe (N) = kQq / r^2
Gravitational and electrical work equations
Respectively:
W (J) = mΔVg
W (J) = qΔVe
Equipotential lines
Where Vg and Ve are the same
Orbital mechanics
In an orbit, a satellite of mass m around a planet (mass M) has an orbital radius r
Escape velocity
To completely leave a system’s gravitational field, you need to go to a distance of infinity. So at infinity, total energy = 0
**escape velocity is the minimum speed you need to reach r = infinity
Orbital speed
A satellite of mass m orbits a central mass M
Magnetic flux
Φ = BA cosθ
where
Φ = magnetic flux
B = magnetic field strength (T)
A = area (m^2)
θ = angle between B and the normal to A
Faraday’s law
ε = −N ∆Φ / ∆t
where
ε = induced emf (V)
N = # of turns in the coil
∆Φ / ∆t = rate of change of magnetic flux linkage
Moving wire in a magnetic field equation
ε = Bvl
where
ε = induced emf (V)
B = magnetic field strength (T)
v = speed of the wire (ms^-1)
l = length of the wire (m)
Alternating current (ac)
Current generated (induced) alternates in direction because of Lenz’s / Faraday’s laws
Maximum power (ac)
Pmax = I0 V0
where
Pmax = maximum power (W)
I0 = maximum current (A)
V0 = maximum p.d. (V)
Average power (ac)
P (line on top) = 1/2 I0 V0
where
P (line on top) = average power (W)
I0 = maximum current (A)
V0 = maximum p.d. (V)
Current graph AC
I(rms) = I0 / √ 2
where
I(rms) = root mean square current
I0 = maximum current (A)
**avg. current = 0
**sin graph (I vs t)
Potential difference (“voltage”) AC
V(rms) = V0 / √ 2
where
V(rms) = root mean square p.d.
V0 = maximum p.d. (V)
**avg. p.d = 0
**sin graph (V vs t)
Ohm’s law for AC
R = V0 / I0 = V(rms) / I(rms)
where
R = resistance (Ω)
V0 = max. p.d. (V)
I0 = max. current (A)
V(rms) = root mean square p.d. (V)
I(rms) = root mean square current (A)
Transformers and rectification
εp / εs = Np / Ns = Ip / Is
where
εp = primary p.d. (V)
εs = secondary p.d (V)
Np = number of turns in primary
Ns = number of turns in secondary
Ip = current in primary (A)
Is = current in secondary (A)
**go from small N to large N (step up)
**gives larger p.d. in secondary
Half-wave rectification (one diode)
In a wave graph, the negative values become zero. (^_ ^_ ^_) (rectified but not smooth)
Adding a capacitor:
(^- ^- ^-) (rectified and smooth)
**happens once per period / cycle
Diode
Only lets current in one direction through
Capacitor
Smoothes the curve because it can charge up while current flows through diode, but when current stops in diode, capacitor discharges into resistor. Smooths out the waves.
It can charge and discharge in a circuit (like a mini battery)
Rectification
The conversion of an alternating current to a direct current
Full wave rectification (two diodes)
You need two diodes and a ‘center tap’ on the secondary (^^ ^^ ^^)
**happens twice per period / cycle
**need twice the number of coils to do thid instead of half-wave rectification
Full wave rectification using a diode bridge
Advantage: need less coils in secondary
Disadvantage: more diodes and more gross looking circuit
shows the same as a normal full wave rectification (^^ ^^ ^^)
Capacitor equation
C = q / V
where
C = capacitance (F)
q = charge (C)
V = p.d. (V)
Parallel plate capacitor equation
C = ε A / d
where
C = capacitance (F)
ε = permittivity
A = area of each plate (m^2)
d = separation between plates (m)
Dielectric
Reduces V, increases C
Discharging capacitors
If the capacitor is charged, when you close the switch it will discharge
The charge in the capacitor equation
q = q0 e^(-t / τ)
where
q = charge remaining (C)
q0 = initial charge (C)
t = time elapsed (sec)
τ = time constant (t)
Time constant equation
τ = RC
where
τ = time constant (t)
R = resistance (Ω)
C = capacitance (F)
Energy stored in a capacitor
E = 1/2 CV^2
where
E = energy stored (J)
C = capacitance (F)
V = p.d. (V)
