charged particle notes

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