3.7.5 Magnetic fields Flashcards
What kind of particles experience a magnetic field?
Moving charged particles
What is Faraday’s Law?
The magnitude of the induced emf is directly proportional to the rate of change in flux linkage
What is Lenz’s law?
The induced emf acts in such a direction to produce effects that oppose the change causing it
What is the formula for flux?
Φ =BA cos(θ) (in a rotating rectangular coil)
What is the formula for flux linkage?
NΦ =BANcos(θ)
What is the equation for emf induced in terms of Faraday’s law and Lenz’s law ?
ε=-N 𐤃Φ/𐤃t
What is an equation for flux in terms of velocity?
𐤃Φ = BA = BLv𐤃t
hence
ε = BLv
What is the formula for Irms?
Irms = I_0 / sqrt(2)
What is magnetic flux?
The force acting per unit current per unit length on a current-carrying conductor placed perpendicular to the magnetic field
What is the definition of the Tesla?
1T; A wire carrying a current of 1A normal to a magnetic field of flux density 1T with force per unit length of the conductor 1N/m
What is the formula for magnetic force on a moving charge?
F=BQv
What is the formula for the radius of a charged particle in a magnetic field?
F = mv^2/r
F=BQv
equate, rearrange, hence
r = mv/BQ
How can centripetal acceleration of a charged object in a magnetic field be found?
F = ma
What are cyclotrons?
A type of particle accelerator that accelerates charged particles from their centre along a spiral path
What are uses of cyclotrons?
Producing medical isotopes (tracers)
Creating high-energy beams of radiation for radiotherapy
What are the components of cyclotrons?
Two hollow semi-circular electrodes (‘dees’)
A uniform magnetic field perpendicular to the electrodes
An alternating p.d., which creates an electric field between the electrodes
Describe the operation of a cyclotron
A source of charged particles is placed at the centre of the cyclotron, then fired into one of the electrodes.
The magnetic field between makes them follow a semi-circular path since it is perpendicular to their motion until eventually they leave the electrode.
P.d. between electrode accelerates the particles across the gap to the next electrode.
Since their speed is now higher, they follow a circular path with a larger radius.
P.d. is then reversed so they accelerate towards the opposite electrode.
This process continues until the particle leaves the cyclotron
Why is there an alternating potential difference between the dees?
Otherwise particles will only accelerate in one direction
What is electromagnetic induction?
The process in which an emf is induced in a closed circuit due to changes in magnetic flux.
When a conductor cuts through field lines it causes change in magnetic flux, which causes work to be done, which is transformed into electrical energy
What is meant by magnetic flux?
The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the flux density
What happens when a magnet is ran through a coil?
When it is not moving there is a zero reading on the voltmeter.
When it begins to move, there is a reading on the voltmeter, it cuts through the field lines, which generates a change in flux. This induces an emf in the coil.
When the magnet is taken out of the coil, emf is induced in the opposite direction, so voltmeter shows reading with the opposite sign.
Increasing the speed of the magnet induces an emf with a higher magnitude.
What are the factors that affect the size of the induced emf through a circular coil?
The speed of the magnet
The number of turns on the coil
The strength of the bar magnet
(increasing all will increase emf)
What is the random formula for a conductor moving through a magnetic field?
∆Φ = BA = BLv∆t
What is the formula for flux linkage of a rotating coil in a magnetic field?
NΦ = BAcos(ωt)
where ω = θ/t
