Magnetic fields + Induction Flashcards
Magnetic field in a bar magnet
Strongest at its ends - “north and south” seeking poles
Field line/line of force is a line along which a north pole would move in the field
Why is the North pole south
Magnet needle points to North pole, which means its actually a south seeking pole
Motor effect
When a current carrying wire is placed at a non zero angle to the lines of force of a magnetic field, it experiences a force due to the field, which is perpendicular to the lines of force and wire.
F=BILsinθ where θ is the angle between the lines of force of the field and the wire
Explaining T = BAncostheta
Right hand grip rule
Curl hand n point thumb in direction of CONVENTIONAL current, curve of fingers shows direction of magnetic field produced by moving current
Magnetic field inside a solenoid
Assumed to be uniform
Faraday’s law
Magnitude of induced emf is directly proportional to the rate of change of magnetic flux linkage
ε = -ΔNΦ/Δt (-ΔNBAcosθ/Δt)
Importance of negative in Faraday’s law
Indicative of Lenz’ law - direction of induced emf acts to oppose the change that caused it.
Lenz law w relation to energy conservation (using bar magnet in coil example)
If coil didn’t repel magnet, it would attract and accelerate the magnet - energy from nothing.
Moving magnet requires mechanical work - equals electrical energy produced in the coil. If pole wasn’t opposite, no conservation
Also if poles were opposite, wld pull magnet in faster, which in turn wld generate a greater emf, energy from nowhere
Why does a current carrying wire experience a force in a magnetic field
The electrons are pushed to one side by the force of the field.
F=BIL for charged particle leading to F=Bqv
L = vt - movement of charge in time t - equivalent to flow of current Q/t in a wire length L
For a charged particle moving across a uniform magnetic field at a speed v perpendicular to the lines of force of the field, force on the particle given by F=Bqv
(Bqvsintheta since u want component of motion perpendicular to lines of force)
Field cld be non uniform
Explanation of why hall voltage is proportional to B
Hall probe - slice of semiconducting material placed in a circuit, magnetic field with lines of force perpendicular to slice. Electrons are deflected down/up to one side of the slice - causing a potential difference (Hall voltage), once is created, force due to mg field = force due to electric field created by hall voltage – QV/d = BQv (no deflection of oncoming electrons)
where d is distance between top and bottom slice.
Vh = Bvd - for a constant current, v is constant so Vh proportional to B
Edit to clarify condition that hall voltage is reached
Conditions for uniform circula acceleration
Particle must be moving in a circle - net acceleration towards the centre of gyration
Electron gun (Thermionic emission)
Electrically heated filament near a positively charged anode - attracts electrons emitted by the filament (thermionic emission).
Electrons pass through small hole in anode to form beam. Greater pd between anode and filament - higher speed of electron when anode reached so faster beam (more power nhf)
Cyclotron + why T is constant (+ exception)
https://www.youtube.com/watch?v=m2jp0klZHEE
Time taken to complete a semi circle = πr/v = mπ/BQ
(Provided that the speed stays much less than the speed of light c)
Electromagnetic induction + induced emf rules
Occurs when a current carrying conductor cuts across the lines of force of a magnetic field, if the wire forms a closed circuit, the induced emf forces electrons around the circuit.
No emf induced in wire if wire is parallel to lines of force as it moves as it moves through the field. Wire must cut across lines of force.
When relative motion ceases, induced emf is 0
Rate of energy transfer from source of emf to other components of the circuit = induced current x emf
How to increase size of induced emf
- Move wire faster
- Use stronger magnet
- Making wire into coil, and
pushing magnet in and out
through it
Right hand dynamo rule
First finger field
Second finger current
Thumb - direction of motion of conductor
riGht for Generator
Magnetic field inside solenoid assumed to be
Uniform
Lenz’ law
Direction of induced current is always to oppose the change that causes the current
Calculating induced size of induced emf for a conductor length L moving a distance s in time t perpendicular to a uniform magnetic field
Motion relative to mg field creates induced current, which produces an opposing force BIL, in order to continue at same speed, there must be an opposing force = BIL. Work done by opposing force through a displacement s = BILs, as W=VIT
ε = BIΔs/Δt
LΔs = area swept out so
ε = BA/Δt
Magnetic flux (φ) + flux linkage
Product of B perpendicular to area swept out by conductor = BAcosθ
(θ is the angle between lines of force and NORMAL to surface swept out)
Unit is the “weber” = Tm^2
Flux linkage through a coil of N turns =NBAcosθ
Note that flux density is flux per unit area passing at right angles through the area
ε = Δφ/t
Different cases for flux linkage
Max (NBA) when magnetic field is perpendicular to coil face
when turned through 180, is -NBA.
When magnetic field is parallel to coil face - NBA = 0 as no field lines pass through the coil area.
Faraday’s law for electromagnetic induction
ε = -NΔφ/t
All forms of Faraday’s law
consider a conductor length l part of a complete circuit cutting ppdly lines of flux density B
Experiences force BIL due to carrying current, opposing motion. Work done = FΔs = BILΔs. Charge transfer in this time is IΔt - using ε = W/Q
ε=BAΔ/t (A = l.s)
For a moving conductor, ε=BLΔs/t === BLv
for a moving magnetic field
ε= ANΔB/t where N is the number of turns on coil
Explaining how emf is induced in a fixed coil in a changing magnetic field
If current in solenoid changes, emf is induced as magnetic field through the coil changes, so there is a change in flux linkage, inducing an emf.
NΦ = BAN - Suppose flux linkage changes in time Δt to from B to (B+ΔB)
Magnitude of induced emf = NΔΦ /Δt = ANΦΔB/Δt
AS B IS PROPORTIONAL TO CURRENT IN SOLENOID, magnitude of induced emf is proportional to the RATE OF CHANGE OF CURRENT - just remember
Rate of change of flux per second for a rectangular coil length l width w entering a uniform magnetic field
Time taken for coil to fully enter field (from front face touching) = w/v. During this time, flux linkage increases from 0 to BNlw
therefore rate of change of linkage = BNLv (as coil enters the field)
Once coil is completely in the field, flux linkage doesn’t change, so induced emf is zero. (Induced emf from leading side is cancelled by trailing) [BAcosθ isn’t changing]
How to make a dc generator
Swap SLIP rings with a SPLIT ring - emf doesn’t change polarity as connections between split rings and contacts switch every half cycle
Emf as a function of angle of coil as time
ε=ε₀sin(ωt)
ε₀ is peak emf
Flux = BANcosωt ω is with frequency of rotation of coil
induced emf a maximum when coil cuts at right angles to field lines, at this point, ε₀ = BLv, where v is linear velocity, and L is length of conductor within field, so total induced emf is 2BLv
v also equal to ωd/2 where d is width of coil (distance from centre of gyration)
Back emf
emf induced in a motor as the flux linkage through the coil changes, acts against applied pd according to Lenz’ law. Induced emf proportional to speed of rotation of motor. V-ε=IR where I is current through motor and R is load resistance. Low speed - current high as back emf is low.
Multiplying equation by I gives power relationship
Frequency of an alternating current
The number of cycles it passes through a second (charge carriers move one way, then reverse, then reverse again)
What is the mean power over a cycle
Half of the peak power 1/2(I₀)^2R
How ac carries energy
Even though electrons don’t move along, its the electric field that carries the energy
What is the rms current/voltage value of an ac current
The value of dc current/voltage that would produce the same power as an alternating current through the same resistance
I/V₀/sqrt2
SI unit for flux
Weber or Tesla metre^2
Drawing a graph of emf when given graph of b/t
Take into account sign - a positive B will cause a negative induced emf due to Lenz’ law
Ways of increasing emf
- use a stronger magnet
- use a coil with more turns
- use a coil of greater area
- place a soft iron core in the coil
- use a larger amplitude of oscillation
of the magnet.
Pulses in coil across rotating magnetic axle points
Direction of induced emf (or current) opposes
the change that produces it.
* A pulse is produced as a magnet approaches
and leaves a coil.
* Forces on a magnet repel it as it approaches
and attract it as it leaves.
* Current therefore flows one way as the
magnet approaches and the opposite way
as it leaves.
Flux linkage units
Weber turns
Calculating max rate of change of flux from a motor
Calculate pd when not rotating,then find back emf by taking difference in voltage when not rotating vs rotating. emf = n(rateorchange…) etc
How a transformer can step down voltage
The alternating voltage, Vin, supplied to
the input causes an alternating current in
the primary coil
* The ac in the primary coil produces an
alternating magnetic flux in the core
* This alternating flux passes through the
secondary coil
* The induced emf, Vout, in the secondary
coil is proportional to the rate of change
of flux linkage
* There are fewer turns on the secondary
than on the primary, so Vout < Vi
Reasons why a transformer might be inefficient
- Thermal energy losses caused by the
currents in the coils, which have resistance - Energy is required to magnetise,
demagnetise and re-magnetise the core - Eddy currents induced in the core cause
thermal energy losses in the core - Imperfect flux linkage: not all the magnetic
flux produced by the primary coil passes
through the secondary coil
P
IrmsxVrms
Irms^2R etc
Back emf in transformers
Alternating flux from primary coil produces back emf in primary coil as well as emf in secondary coil - Acts against primary voltage making primary current very small when secondary is “off”. When secondary current is on, the magnetic field produced opposes the back emf (what induced it), therefore reducing back emf, so primary current is larger than when secondary current is “off”
Why are transformers almost 100% efficient
Low resistance windings to reduce power wasted due to heating effect of current
Laminated core which consists of iron layers separated by layers of insulator (current would flow across coils, path of least resistance, rather than along wire). Induced currents, aka eddy currents, are reduced so magnetic flux is high as possible. Also heating effect of induced current reduced
Containing a magnetised SOFT iron core - easily magnetised and demagnetised, reduces power wasted through repeated magne and demagnetisation
Efficiency of national grid
Current required to deliver power P = P/V. Power dissipated through cables = I²R = P²R/V² - Higher value of voltage - smaller value of wasted power compared to transmitted power
How a magnetic pendulum swinging through a magnetic field is heavily damped
Bob cuts through magnetic flux of field, Induces an emf in the bob, causing circular (eddy) currents in the bob, which generates a magnetic field that opposes the og one/ Causes thermal energy losses in the bob, which must come from the Ek of the bob, causing it to slow down rapidly
R decreasing in r=mv/Bq
R decreasing means path is more curved
