The electron beam emerges from the anode of the electron gun on the
axis, but with a divergence of up to 5° from
the axis, as illustrated in figure 2.2. In general a diffuse spot is produced
on the screen, but for certain values of the magnetic field a sharply focused
spot is obtained.
By considering the motion of an electron initially moving at an angle b (where 0 £ b £ 5°) to the axis as it leaves the electron gun, and considering the components of its motion parallel and perpendicular to the axis, derive an expression for the charge to mass ratio e/m for the electron in terms of the following quantities:
Write your expression in the box provided in section 2a of the answer sheet.
A point source of b particles, which emits the b particles uniformly in all directions with a range of velocities, is placed between the centres of the plates, and the same piece of film is exposed under three different conditions:
where V 0 and B 0 are positive constants. Please note that the upper plate is positively charged when V>0 (negative when V<0 ), and that the magnetic field is in the direction defined by figure 2.5 when B>0 (in the opposite direction when B<0 ). For this part you may assume the gap is negligibly small.
Two regions of the film are labelled A and B on figure 2.3. After exposure and development, a sketch of one of these regions is given in figure 2.4. From which region was this piece taken (on your answer sheet write A or B)? Justify your answer by showing the directions of the forces acting on the electron.
Numerical values of the system parameters are given below:
B0 = 6.91 mT V0 = 580 V t = 0.80 mm s = 41.0 mm
In addition, you may take the speed of light in vacuum to be 3.00 × 108 m s-1, and the rest mass of the electron to be 9.11 × 10-31 kg.
Determine the maximum b particle kinetic energy observed.
Write the maximum kinetic energy as a numerical result in eV in the box on the answer sheet, section 2c.
Indicate algebraically the quantities being plotted on the horizontal and vertical axes both on the graph itself and on the answer sheet in the boxes provided in section 2d.
Write your value for the charge to mass ratio of the electron in the box provided on the answer sheet, section 2d.
Please note that the answer you obtain may not agree with the accepted value because of a systematic error in the observations.