- There is a lot of mathematics surrounding magnetism and magnetic forces
- The key equations are:
F = BIL
F = Bqv
- Below are two worked examples demonstrating different situations involving magnetic forces
Calculate the magnetic flux density of the magnet.
- Length, L = 5 cm = 0.05 m
- Current, I = 1.5 A
- Force, F = 0.06 N
This question is about the movement of an electrically charged particle into a magnetic field. An electron enters a magnetic field and moves in an approximately circular path as shown below.
- Explain whether the speed of the proton is the same when entering and exiting the magnetic field.
- The magnetic field has a strength of 0.3 T and the velocity of the electron before entering the magnetic field is 8.6 × 106 m s−1 to the left. Show that the radius of the motion of the electrons is 1.63 cm.
The answer is that the work done by the magnetic force on the charge must be zero
This is because the force itself is at right angles to the velocity
Since the work done is zero, therefore the kinetic energy does not change between entering and leaving the magnetic field
Therefore the speed is the same
- Magnetic field strength, B = 0.3 T
- Velocity of electron (before entering field), v = 8.6 × 106 m s−1 to the left
- Radius of motion to be shown, r = 1.63 cm
- This can be done for the situation since the circular motion is caused by the magnetic force
Step 3: Rearrange the equation to find the radius
qvBr = mv2
qBr = mv
Step 5: State final answer
R = 1.63 × 10−2 m = 1.63 cm in a circular motion