Alvl P2: Magnetic Fields (ch16) Cheat Sheet

Cyclotrons use F = BQv to produce a beam of charged particles
for example: for proton therapy

magnetic fields causes protons to be emitted by the source in the centred to undergo circular motion inside the metal Dees

they use altern­ating currents as the oppositely charged dee causes the protons to be accele­rated across and then back again after flipping the charge again, increasing their velocity and therefore radius.
>every half a cycle the polarity of the dees must reverse in order for the protons to be contin­uously accele­rated across again.

as f is indepe­ndant of r, all protons have the same frequency and time period regardless of radius
> the frequency of AC applied to the dees must match this

used to change the voltage (reduces current and therefore power lost to heat in national grid cables)

- AC primary coil induces altern­ating magnetic field in sort iron core (easily (de)ma­gne­tised)
- this induces a current in the secondary coil
- the side with the most turns (N) has the greater pd (N ∝ v)

equations:

VpIp = VsIs
Ns/Np = Vs/Vp
efficiency = useful­/total x100
rms = Xo/2^1/2


Energy losses:

problem-
--- heat is produce in copper coils when a current flows causing heat loss
solution-
--- use thicker wires (creates lower resist­ance)

problem-
--- some mag flux doesnt pass through the iron core reducing the flux lin of the secondary coil
solution-
--- reduced by keeping coils close/­wound together

problem-
--- eddy currents are induced, due to the mag flux created in coils, opposing the charge that produced it (Lenz's law) causing heat loss in the coil
solution-
--- laminating with insulating material
--- using thin sheets so smaller emfs are induced

a charge in a magnetic field has to be moving to experience a force.

a free charged particle will undergo circular motion in this field.

this is given by F = BQv


for proving frequency is indepe­ndant of radius:

BQv = mw²r
BQwr = mw²r
w = BQ/m
2pi.f = BQ/m therefore indepe­ndant

generators consist of a spinning coil in a magnetic field.

-when the coil is parallel to the field there is no induced emf
-when the coil is perpen­dicular to the field there is induced emf
(the constantly spinning coil allows the induced emf to remain for longer as the field is constantly changing.)

Peak EMF:
E = BANw = 2BLv

EMF at any time:
E =Eo sin(wt) = BANwsi­n(wt)


overhead cables are made from aluminium (light) with steel core (strong).
copper would be too expensive

an emf (and current) will be induced in a wire thats part of a loop if it expere­inces a changing field.

lenz's law > demons­trated by dropping a magnet downa copper pipe.
an eddy current is induced which produces a force that opposes the magnets motion (therefore slowing down as the magnet wants to accelerate down due to gravity the eddy currents create a force upwards slowing it down)


for a moving wire:
- must move perpen­dicular to the field lines
flux = BA therefore flux now = BLd where L is the length of wire in the field and d is the distance in the perpen­dicular direction

for moving loop:
- emf is only induced as it enters­/leaves as this is where there is a change in magnetic field (change in magnetic flux)
- its constant while inside the field

for static coils:
- B must be changed as A is not
- this is done by using an AC current
- if DC is used then the current will only be induced for a short amount of time