1. Movement of Charges
In a Magnetic Field

2. Revision of the Motor Effect
An electric current interacts with a perpendicular magnetic field .
This results in a force.
Direction of the force is given by Fleming’s Left Hand Rule.
Equation:
Sunday, 24 February 2019
Leeds City College

3. Charge in a Magnetic Field
Electron Gun
2500 V
Magnetic Field, B, going into the page
6.3 V a.c.
We find that in a magnetic field, the force acts on a stream of electrons always at 90o to the direction of the movement. Therefore the path is circular.
Consider a charge q moving through a magnetic field B at a constant velocity v. The charge forms a current that moves a certain distance, l, in a time t.
Sunday, 24 February 2019
Leeds City College

4. Force on the Charge F = B I l I = Q t l = v t We know:
Velocity = distance  time
Current = charge  time
F = BIl
The t terms cancel out to give: F = B I l I = Q t l = v t
Sunday, 24 February 2019
Leeds City College

5. Motion in a magnetic field
B field going into the screen
The force at 90 o acts as a centripetal force, keeping the electron in a circular path.
Force always acts at 90 o
Sunday, 24 February 2019
Leeds City College

6. Bear Trap
Remember that the direction of the electrons’ movement is in the opposite direction to the conventional current. So if the electrons are going from left to right, the conventional current is going from right to left.
When using Fleming’s Left Hand Rule, the current is conventional.
Sunday, 24 February 2019
Leeds City College

7. Equation For centripetal force:
The v on the left cancels to get rid of the v2 term on the right:
For a charge in a magnetic field:
Rearranging:
We equate these to give:
Sunday, 24 February 2019
Leeds City College

8. Cyclotron
This is a particle accelerator which relies on a magnetic field to make an electron move out in a spiral.
Electromagnet
Evacuated chamber
Dees
Ion source
Uniform B field
High frequency a.c.
Path of charged particles
From above:
The beam goes out in a spiral, as the particle is getting faster all the time.
Sunday, 24 February 2019
Leeds City College

9. Equation
If a particle of charge q enters one of the dees with a speed v, it will move in a semi-circular path of radius r.
For 1 revolution
Since f = 1/t
Rearranging gives
Therefore:
And rearranging gives us:
From simple linear motion:
And r terms cancel out
Which can be equated:
Sunday, 24 February 2019
Leeds City College