Charged particles
Conventional current flows from +ve to -ve terminal as it is the flow of positive charge and
opposes flow of electron
Factors affecting size of force on a moving charge in a uniform magnetic field:
1. Magnetic flux density (B)
2. Charge on particle (Q)
3. Velocity of particle (v)
Force (on a moving particle at right angles to magnetic field)
F = BQv
If the particle is moving at an angle, F = BQv sinθ (direction of force can be determined using
Flemings left hand rule)
Derivation of BQv
I = Q/t
Substitute into F = BIL
F = BQL / t
Speed = l / t
So, F = BQv
For electrons we can write it as F = Bev where e is = 1.6 x 10−19
The constant force due to the magnetic field is always perpendicular to the velocity of the
electron. Hence, F acts as a centripetal force.
Magnetic force provides centripetal force, so
Bev = m v 2/r
mv
Radius of orbit (r) =
Be
This can also be written as p = Ber where p is momentum since momentum = m x v
mv
The equation r = shows that:
Be
r ∝ v (greater the particle speed, greater the orbital radius)
r ∝ m (greater the particle mass, greater the orbital radius)
r ∝ p (greater the momentum, greater the orbital radius)
1
r∝ (greater the charge on particles, smaller the orbital radius)
q
1
r ∝ (greater the magnetic field B, smaller the orbital radius)
B
charge to mass ratio
uses the equation for electron travelling in a circle in a magnetic field
mv e v
rearrange r = to give =
Be m Br
velocity selector
A device consisting of perpendicular electric and magnetic fields where charged particles
with a specific velocity can be filtered
Conventional current flows from +ve to -ve terminal as it is the flow of positive charge and
opposes flow of electron
Factors affecting size of force on a moving charge in a uniform magnetic field:
1. Magnetic flux density (B)
2. Charge on particle (Q)
3. Velocity of particle (v)
Force (on a moving particle at right angles to magnetic field)
F = BQv
If the particle is moving at an angle, F = BQv sinθ (direction of force can be determined using
Flemings left hand rule)
Derivation of BQv
I = Q/t
Substitute into F = BIL
F = BQL / t
Speed = l / t
So, F = BQv
For electrons we can write it as F = Bev where e is = 1.6 x 10−19
The constant force due to the magnetic field is always perpendicular to the velocity of the
electron. Hence, F acts as a centripetal force.
Magnetic force provides centripetal force, so
Bev = m v 2/r
mv
Radius of orbit (r) =
Be
This can also be written as p = Ber where p is momentum since momentum = m x v
mv
The equation r = shows that:
Be
r ∝ v (greater the particle speed, greater the orbital radius)
r ∝ m (greater the particle mass, greater the orbital radius)
r ∝ p (greater the momentum, greater the orbital radius)
1
r∝ (greater the charge on particles, smaller the orbital radius)
q
1
r ∝ (greater the magnetic field B, smaller the orbital radius)
B
charge to mass ratio
uses the equation for electron travelling in a circle in a magnetic field
mv e v
rearrange r = to give =
Be m Br
velocity selector
A device consisting of perpendicular electric and magnetic fields where charged particles
with a specific velocity can be filtered
