The picture above shows part of a mass spectrometer that can be used to measure

Question

The picture above shows part of a mass spectrometer that can be used to measure molecular charge-to-mass ratios. A charged molecule (orange circle) is ionized and accelerated through an electric potential difference into a region with a uniform magnetic field. Here the magnetic field points out of the screen. The field makes the positively charged molecules undergo circular motion as shown. By adjusting the voltage difference between the plates, one can change the radius of curvature of the charged particles until they reach the detector. For a magnetic field of B = 1 mT and a spacing between the entrance and exit holes of d = 10 cm. what is the potential V (in mV) required to detect 0_2+? (You may assume that the mass of the O_2+ ion is 2.65e-26 kg) The right and left end wires of two circuits are separated by a distance d-3mm. If L - 22 cm, V1 = 8 V, V2 = 8 V, R1 = 8 Omega and the magnetic force between the circuits is F = 10 muN, then what is the resistance (in ohms) of R2? (This problem is inspired by Problem 32.35 of Knight's 3rd edition).

Explanation / Answer

ion will have travel in circular path with radius of d/2 = 5cm = 0.05 m

for circular motion,

q v B = m v^2 / r

1.6 x 10^-19 x 1 x 10^-3 = 2.656 x 10^-26 x v / 0.05

v = 301.20 m/s

and kinetic energy gain = q V

2.656 x 10^-26 x 301.20^2 / 2 = 1.6 x 10^-19 V

V = 7.53 x 10^-3 volt Or 7.53 mV

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