Here is a recap of in-class problems/questions dealing with charged particles accelerating across a potential difference and/or being steered or deflected by Electric or Magnetic fields. You might also want to review the textbook’s Assigned problems: Ch.19: P 56, 76 Ch.20: P 17,18 Ch.22: P 17 Quiz# 2 deals with answering questions about (and calculating values for) charged particle beams being accelerated and deflected by E and B fields.
If the effective field is E =800,000 N/C over a gap length of 2.5 cm, what is the electron’s final velocity, v ? Electron Gun Heated filamentPositively charged can (1.6 C)(8 10 5 N/C) 9.11 kg 0 + 2(1.405 m/s 2 )(0.025 m) m 2 /s 2 v 8.38 10 7 m/s 1. One method you can use: See your class notes for Friday, September 5
E = 800,000 N/C d = 2.5 cm, 1 e = 1.60 C v final ? How much energy is given to each electron? What voltage difference do the electrons experience jumping the gap? An electron with this much energy, must be moving how fast? 2. Another method See your class notes for Monday, September 7
v o = 8.4 10 7 m/sec m e = 9.11 kg 1 e = 1.60 C E max = ? -e-e 2 centimeters 0.3 cm If the beam then enters the center of the 0.3cm gap between two electrostatic plates, 2cm in length, what is the maximum E field that will still allow the electrons to escape the opposite side? See your class notes for Friday, September 5
2 centimeters 0.3 cm -e-e vo vo x = v ox t + ½a x t 2 y = v oy t + ½a y t Time within plates: t= (horizontal distance)/(horizontal speed)=2 cm/ v o Maximum tolerable acceleration up then comes from d = (1/2)at 2 using that same time and noting from the center d=(1/2)0.3cm: 0.15 cm = (1/2) a (2.38 sec) 2 a = m/sec 2 Answer: E = 301,541 N/C
v= /2qV/m R=? Mass spectrometer: Show that any charged ions drifting from the vaporization chamber (far left) are launched to this final speed by the accelerating potential. Then show that the radius of curvature inside the B-field should be: See your class notes for Wednesday, October 1