Magnetic fields Flashcards
When using Fleming’s left hand rule for moving charged particles, what happens if the charge is negative?
Point your second finger in the direction opposite to its motion
What are the units for magnetic flux?
Wb
What is the equation for the force on a particle in circular orbit?
F = mv²/r
What is the equation for the radius of the circular path of a charged particle in a magnetic field?
r = mv/BQ
Where:
* r = Radius (m)
* m = Mass (kg)
* v = Velocity (m/s)
* B = Magnetic flux density (T)
* Q = Charge (C)
Derive the equation for the radius of the circular path of a charged particle in a magnetic field.
Force on a charged particle in a magnetic field:
* F = BQv
Force on a particle in circular orbit:
* F = mv²/r
Therefore:
* BQv = mv²/r
* r = mv/BQ
In magnetic fields, what is φ?
Magnetic flux
What is the equation for the force experienced by a charged particle in a magnetic field?
F = BQv
Where:
* F = Force (N)
* B = Magnetic flux density (T)
* Q = Charge on particle (C)
* v = Velocity of particle (m/s)
Describe the structure of a cyclotron.
-Two hollow semi-circular electrodes with alternating potential difference.
-Slight gap between them.
-Uniform magnetic field applied perpendicular to the plane of the electrodes.
Describe how a cyclotron works.
-Particle (charged) is fired into one of the electrodes
-The magnetic field makes it flow a semi-circular path and return to the gap between electrodes
-The potential difference between them creates an electric field that accelerates the particle across the gap
-The velocity in now higher, so the particle takes a path with a larger radius before leaving the other electrode
-As it exits, the potential difference is reversed at this point so that the electric field is reversed and therefore the particle can accelerate across the gap
-This repeats as the particle spirals outwards, increasing in speed, before exiting the cyclotron
If p.d wasn’t alternating what would happen to the particle in a cyclotron?
It would slow down after leaving the second electrode
What is the equation for magnetic flux?
φ = BA
Where:
* φ = Magnetic flux (Wb)
* B = Magnetic flux density (T)
* A = Area (m²)
What happens when a conductor is moved in a magnetic field?
If it cuts through field lines, an emf is induced in the conductor:
The electrons in the rod will experience a force, which causes them to accumulate at one end of the rod - this induces an emf across the ends of the rod = electromagnetic induction.
Why is an emf induced in conductor when it cuts through magnetic field lines?
The electrons experience a force, so they accumulate at one end of the rod
This induces an emf between the positive and negative ends of the rod
What is electromagnetic induction?
When an emf is induced in a conductor that cuts through magnetic field lines.
How can you induce an emf in a flat coil or solenoid?
-Moving the coil towards it away from the poles of the magnet
-Moving a magnet towards or away from the coil
An emf is induced in a conductor when what is changing?
The magnetic field
What is magnetic flux linkage?
The product of the magnetic flux passing through the coil and the number of turn in the coil they cut the flux.
What are the units for magnetic flux linkage?
Wb turns
What is the equation for magnetic flux linkage when the coil is perpendicular to the field?
Nφ = BAN
Where:
* Nφ = Magnetic flux linkage (Wb turns)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* N = Number of turns
What is the equation for magnetic flux when the coil is not perpendicular to the field?
φ = BAcosθ
Where:
* φ = Magnetic flux (Wb)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* θ = Angle between the field and the normal of the plane of the loop
(NOTE: Not given in exam!)
What is the equation for magnetic flux linkage when the coil is not perpendicular to the field?
Nφ = BANcosθ
Where:
* Nφ = Magnetic flux linkage (Wb turns)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* θ = Angle between the field and the normal of the plane of the loop
Why is BANcos used instead of BAN?
What rule do we have to take into account?
When flux linkage isn’t perpendicular to coil of wire, we need to resolve for horizontal component because that is where you get to max force (perpendicular):
What does the rate of change of flux tell you?
How strong the emf will be in volts:
What can’t you do with Nφ = BAN
Describe what the difference is between:
* Magnetic flux density
* Magnetic flux
* Magnetic flux linkage
Magnetic flux density - The number of magnetic field lines per unit area in a magnetic field
Magnetic flux - The total number of field lines passing through a given area.
Magnetic flux linkage - The magnetic flux multiplied by the number of coils.
What is the symbol for magnetic flux linkage?
Nφ
State Faraday’s law.
The magnitude of the emf induced in a conductor is directly proportional to the rate of change of flux linkage.
Give the equation for Faraday’s Law.
ε = NΔφ/Δt
Where:
* ε = Magnitude of induced emf (V)
* Nφ = Magnetic flux linkage (Wb turns)
* t = Time (s)