chapter 23 - magnetic fields Flashcards
magnet vs magnetic material
magnet is magnetised
magnetic material has the capacity to be magnetised (and demagnetised)
magnetic field lines
- arrow shows direction
- = spaced + parallel shows uniform field
- where stronger field is closer
- N>S
motor effect
force on a current carrying wire due to a magnetic field at a non zero angle (not parallel)
size depends on
- current size
- strength of magnet
- length of wire
- angle between wire and field (min at 0 max at 90)
dircetion of force depeneds on direction of field and current (flemmings left hand)
flemmings left hand rule
can use to predict the direction of motor force
thumb = motion
first finger = field
second finger = current
right hand grip rule
thumb is current
fingers are magnetic field
or other way round in a solenoid
magnetic flux density (B)
(field strength)
force per unit length per unit current on a current carrying conductor perp to a magnetic field
- shown by closeness of field lines
measured in Tesla
Tesla
unit of magnetic flux density (B)
the strength of flux density that produces a force of 1N in a wire of 1m with 1A flowing perp to the field
force on a wire carrying a current at an angle to a field
if perp
F = BIL
if not
F = BILsinθ
direction of field inside solenoid
use right hand grip rule in reverse to find direction of field in solenoid
(inside a solenoid field lines are parallel and uniform)
magnetic field
a region in which a piece of ferromagnetic material or a magnet or a current carrying conductor or a moving charge experiences a force
- exist around permenant magnets or current carrying conductors
- density of field lines shows strength
- parallel lines = uniform field
force on moving charges in a magnetic field
F = Bqv
a charged particle entering a magnetic field perp to the field direction experiences a centripetal force so moves in a circle
mv^2/r = Bqv
r = mv/Bq
helical path of an electron
if electron enters field at an angle resolve the velocity so in one direction it moves circularly but in the other v is parallel to the field so moves in a straight line
- moves like a corkscrew
accelerators
- single stage = one electric field
- multi stage = synchronised fields
electron goes through magnetic field once it goes through it the field dircetion switches so its repelled from the previous one and attracted to the next - the longer the tube the greater the acceleration
curved accelerators
same as a linear accelerator but with curved fields
increased radius = increased acceleration
curved path means particles can accelerate through gaps more than once
+ particles can reach higher energy as can keep going round
+ alternating field keeps giving them more energy
velocity selector
- uses electric and magnetic fields to select charged particles of a specific velocity
- applies a magnetic field perpendicular to the electric field
Fe = Fm
Eq = Bqv
v = E/B
time period of the orbit of one electron
r = mv/Bq
v = 2𝞹r/T
T = 2𝞹m/Bq
hall probe
- measures magnetic flux density
- Vh = BI/nbq
where b is the thickness
hall effect
a potential difference is crated across a semi conductor due to a magnetic field across it
- when a wire is put in a field F(B) occurs due to the magnetic field so electrons move down
- as electrons build up on the edge they’re forced to
- an electric field is created which has a force F(E) forcing the electrons upwards
- when in equilibrium F(E) = F(B)
- electrons then travel through the wire in a straight line
voltage due to hall effect
V = IB/nbq
I = nAqv
F(B) = Bqv
F(e) = EQ
F(B) = F(E) Bqv = Eq
E = Bv = V/d
V = Bvd = BId/nAq = BI/nbq
where b = the thickness
electromagnetic induction
- when a wire cuts a magnetic field it produces an induced emf across the wire
- if the wire is part of a complete circuit current flows
increase emf by - increasing speed
- increasing field strength
- increasing length
magnetic flux
is the produce of magnetic flux density and area
= BA
measured in weber (Wb)
magnetic flux linkage
= NBA
measured in Weber turns
product of magnetic flux and number of turns
lenz law
the direction of the induced emf due to a change of flux linkage is such that it will oppose the change of flux producing it
- if it was opposite it would attract so accelerate greatly breaking the law of conservation of energy
faradays law
the magnitude of the induced emf in a circuit is = to the rate of change of flux linkage in a circuit
ε = dNBA/ dt
deriving faradays law
WD = Fs
WD = BILs
Q = It WD = VQ
V = WD/It = BILs/It = BLs/t = BA/t
flux linkage graphs and emf graphs
emf graph is the gradient function of the flux linkage graph
ac generator
- consists of a coil spun in uniform field
- when coil spins at steady rate flux linkage changes continuously
- when coil is at θ to the field flux linkage = NBAcosθ
θ = t/T *2𝞹 = 2𝞹ft = wt
emf = derivative of flux linkage d/dt of NBAcos(wt) = NBAwsin(wt)
peak emf induced
V =NBAwsin(wt)
max when sin(wt) = 1
V = NBAw
slip/split ring commutator
slip - generates ac - solid - doesnt change
split - generates dc - split - changes every half turn
3 phase generator
spinning magnet in middle with coils outside
emf induced in pair of coils
each pairs wave is shifted
using 3 waves gets 3 phases of emf maximising efficiency
transformers
step up - increase pd
step down - decrease pd
consists of a primary coil and secondary coil connected by a soft iron core
Np/Ns = Vp/Vs = Is/Ip (if 100% efficient)
emf in terms of v
V = BLs/t = BLv
eg satellite dragging conductive teather through magnetosphere can generate emf
why transformers not 100% efficient
- energy loss from current flowing - resistance in wire causes heating effect Plost = I^2R decrease loss by increasing A and decreasing resistivity
- energy loss from magnetic losses - prevent by putting coils close with soft core - ensures as much if flux as possible is passed onto secondary coil
- energy loss from magnetising/ demagnetising core - increases temp - use material easily magnetised/ demagnetised
- eddy currents created in iron core due to magnetic field causing electrons to move - laminated (insulator between layers) prevents this
transformer efficiency
IsVs/IpVp *100
power transmission lines
step up to increase voltage which decreases current reducing energy losses due to heating effect
P loss = I^2R (pd lost is not the same as overall pd so cant use P = IV)
finding magnetic flux density in the lab
- place magnets opposite each other on a mass
- put a wire in-between them
- measure force using the balance = W
- B = F/IL
- zero balance when no current in the wire
- then apply a current
