9Motion of a charged particle in the magnetic field

Structured questions.

1.   A proton of kinetic energy 15 keV travelling at right angles to a magnetic field describes
a circle of radius of 5.0 cm. The mass of a proton is 1.7 ´ 10⁻²⁷ kg.

a    Show that the speed of the proton is 1.7 ´ 10⁶ m s⁻¹.                                                           [3]

b    For this proton, calculate the centripetal force provided by the magnetic field.                      [3]

c    Determine the magnetic flux density of the magnetic field that keeps the proton moving
in its circular orbit.                                                                                                            [3]

d    How long does it take for the proton to complete one orbit?                                                 [2]

2.   The diagram shows a velocity-selector for charged ions. Ions of speed v emerge from the slit.

      The parallel plates have a separation of 2.4 cm and are connected to a 5.0 kV supply.
A magnetic field is applied at right angles to the electric field between the plates such
that the positively charged ions emerge from the slit of the velocity-selector at a speed of 6.0 ´ 10⁶ m s⁻¹. Calculate the magnetic flux density of the magnetic field.                                                   [6]