Please SHOW ALL WORK AND FORMULAS, IN HANDWRITING IF POSSIBLE. THANKS 15. The de
ID: 1460481 • Letter: P
Question
Please SHOW ALL WORK AND FORMULAS, IN HANDWRITING IF POSSIBLE. THANKS
15. The device shown above (a spectrometer) accelerates an ion from rest through a potential difference E = 800 V between two parallel plates as shown above. The ion has a charge of magnitude 2e. The ion then enters a region containing a uniform magnetic field B = 0.075 T which is constant in magnitude and perpendicular to the plane of the path of the ion. The particle curves in a semicircular path and strikes a detector as shown above. The mass of the ion is 6.64 X 10-27 kg. Recall that e = 1.602 X 10-19 C. (25 points)
i) What is the sign of the charge on the ion? How do you know?
ii) In what direction must B point in order to produce the trajectory shown? Explain your answer.
iii) Calculate the speed of the ion as it enters the region of the magnetic field.
iv) What is the magnitude of the force on the ion as it enters the region of the magnetic field?
Explanation / Answer
i) it must be a positive charge ,Since it was accelarating ,it was attracted by the negative terminal of the battery
ii) B must be outside of the screen inaccordance with the Fleming's left hand rule
iii) Apply q*V = 0.5*m*v^2
2*1.6*10^-19 * 800 = 0.5*6.64*10^-27*v^2
v = 27.76*10^4 m/s
iv)
radius r = m*v/(q*B) = (6.64*10^-27*27.76*10^4)/(2*1.602*10^-19*0.075) = 76.7 mm
required distance is 2r = 153.4 mm