Magnetic Fields - Structured Questions
Q2. The diagram below shows the path of protons in a proton synchrotron.
The protons are injected at a speed of 1.2 × 105 ms1 and a magnetic field is applied to make them move in a circular path.
(a) Calculate the magnetic flux density of the field required for protons to move in the circular path when their speed is 1.2 × 105 ms1.
∴ BQv = mv2/r
B = mv/rQ
B = 1.67 × 10−27 × 1.2 × 105 /(120 x 1 .6 x 10-19) = 1.04 × 10−5
B = 1.0 × 10−5 T
This magnetic field must act upwards, out of the plane of the page (Fleming's left-hand rule)
(b) Explain how the magnetic flux density required to maintain the circular path has to change as the kinetic energy of the protons increases.
As the kinetic energy of the protons increases the radius of the path they take would increase if the magnetic field strength remained steady. The magnetic flux density therefore has to increase because in a path of constant radius (using the same charged particles) magnetic flux density B ∝ v
(5 marks)