Magnetism, EM induction and AC Flashcards
Right hand grip rule
Fingers: field
Thumb: current
Force formulas
Force on charge carrying wire
F = B I L sinθ
Force on charged particle
F = B Q v sinθ
Magnetic flux density meaning
Force experienced by a straight current carrying conductor at right angles to that field per unit length and unit current
1 Tesla is…
when a current carrying wire of 1m length with 1A current placed at at a right angle to a magnetic field experiences a force on 1N
Left hand rule
Thumb: force
Index: field
Middle: current
Force goes in opposite direction if electrons are considered instead of current
Centripetal force provided by magnetic force
Fc = Fn
mv²/r = B Q v sinθ
r = m v sinθ / Bq
Hall effect formulas
Vʜ = I B / n q t
I is current
B is magnetic flux density
n is number charge density
q is elementary charge
t is thickness of the waver
Conservation of energy with Hall effect;
lots of formulas
Fe = q E
q is elementary charge
E is electric field strength
W = Fe x d = Vʜ x q
v = E / B
v (velocity of charged particle)
E (electric field strength)
B (magnetic field strength)
E = V / d
E (electric field strength)
V (pd between 2 points)
d (distance between 2 points)
Lenz’s law definition
any induced current or induced emf will be established in a direction so as to produce effect which oppose the change that is producing it
Right hand rule generator edition
Thumb: force applied to cause motion
Index: magnetic field
Middle: current inside conductor
Used when force makes current
Lenz’s law conservation of energy and key formula
W = F x
W = P ∆t
ε = B L v N
ε is emf across conductor
Magnetic flux linkage
ψ = B A cosθ N
ψ flux linkage
B magnetic field density
A area linked to magnetic field
N number of loops
Faraday’s law definition
magnitude of induced emf is proportional to rate of change of magnetic flux linkage
Faraday’s law emf formulas
ε = - [ ∆ψ / ∆t ] N
Generating AC currents
flux
ψ = BA cos(ωt)
emf
εₜ = ε₀ sin(ωt)
pd (with closed circuit)
Vₜ = V₀ sin(ωt)
current
Iₜ = I₀ sin(ωt)
(V = RI and θ = ωt)
Use cos if variable starts at max when crossing origin and use sin if variable starts at zero when crossing origin
AC- Power formulas
peak power:
P₀ = V₀² / R
or
P₀ = I₀² x R
mean power:
Pₐᵥ = 0.5 x V₀² / R = V²ᵣₘₛ / R
or
Pₐᵥ= Iᵣₘₛ² x R = 0.5 x I₀² x R
root mean square:
Vᵣₘₛ = V₀/√2
Iᵣₘₛ = I₀/√2
Transformers
Vs/Vp
Ns/Np
=
Ip/Is
Flux
Amount of magnetism, unit: Wb
Flux density
How tightly packed together are the field lines
B, unit: T (tesla)
Direction of current into or out of plane
Dart method
Dot: into plane
Cross: out of plane
Additional flux formula
B = mg/IL
Emf and flux graphs against t - for coil entering and exiting uniform magnetic field
phi / t
zero grad at zero
constant positive grad
zero grad at constant
constant negative grad
zero grad at zero
- emf / t
zero grad at zero
vertical upwards
zero grad at constant
vertical back to zero
zero grad at zero
vertical downwards
zero grad an negative constant
vertical back to zero
zero grad at zero
Stationary coils
In order to induce emf, flux density over time must be changing as area of coil remains constant
Flux linkage
Same as flux but with multiple turns hence formula is
Flux linkage = BAN
Eddy currents and transformers
By laminating or cutting transformer into layers this reduced eddy currents and heating effect to increase efficiency of transformer
Eddy currents
Eddy currents are electric currents that circulate within a conductor and are induced when a conducting material is exposed to a changing magnetic field. Eddy currents can create resistance and heat within the conducting material.
AC generation and flux
flux is zero and emf is at a maximum when coil is parallel to field
flux is at a maximum and emf is zero when coil is perpendicular to the field
Flux time and emf time graph for AC generation
phi / t
sinusoidal graph where peak at max and min are equal to BAN and -BAN respectively
emf / t
sinusoidal graph where peak is at zero for phi and zero is at peak for phi, max is ε₀
emf and flux (linkage) are 90º out of phase
AC and diodes
Voltage with dc current gives full sinusoidal graph
Half wave rectification: With a diode it gives sinusoidal graph discarding any negative directions
Full wave rectification: 4 diodes in a diamond arrangement which gives the half wave rectification graph excluding the gaps
Smoothed rectification with capacitor: initial sinusoidal curve into ripple (produced with capacitor and resistor)
Magnet in free fall through solenoid graph
ε against t
increasing grad
decreasing positive grad
zero grad
decreasing negative grad
zero
sharp negative grad and smooth curve into sharp positive grad back to zero
Vf > Vi
|+ε max| < |- ε max|
Time for proton to complete a full circle
If field is large enough:
T = 2πr / v
r = mv/Bq
Additional formulas from Kwon’s notes
q/m = v / rB
e/m = 2V / r²B²
ε = ω N B A sinθ
Recall:
ω = 2πf
